MATLAB m-files for Figures for Applied Partial Differential Equations Text by Richard Haberman

The figures for the fourth edition (2004) of my text  Applied Partial Differential Equations (with Fourier Series and Boundary Value Problems) published by Prentice-Hall were prepared using MATLAB 4.2. Please feel free to copy (download) any or all of these MATLAB m-files. Just right click on the following links. For examples, F234.M is the MATLAB m file for Figure 2.3.4. and F1244.M is for Figure 12.4.4.

 

Chapter 2

F234.M,F235.M,F253A.M,F253B.M,F253C.M,F253D.M

Chapter 3

F338A.M,F338B.M

Chapter 4

F441A.M,F441B.M,F441C.M

Chapter 5

F581.M,F582.M,F583.M,F584.M

Chapter 6

F621.M,F635A.M,F635B.M,F636.M,F638.M,F641.M,F642.M,F643.M

Chapter 7

F732A.M,F732B.M,F732C.M,F771.M,F781.M,F782.M,F783A.M,F783B.M,F783C.M,F783D.M,F783E.M,

F792.M,F7101.M

Chapter 9

F934.M,F935.M,F936.M

Chapter 10

F1032.M,F1041.M,F1042.M,F1043.M,F1044.M,F1062.M,F1064A.M,F1064B.M

Chapter 11

F1122.M,F1131.M

Chapter 12

F1221.M,F1222.M,F1223.M,F1231.M,F1232A.M,F1232B.M,F1232C.M,F1233.M,F1234A.M,F1234B.M

F1244.M,F1263.M,F1264A.M,F1265B.M,F12610A.M,F12610B.M,F12612.M

Chapter 14

F1421.M,F1432.M,F1443.M,F1451.M,F1452.M,F1463.M,F1464.M,F1465.M,F1468.M

F1471.M,F1472.M,F1473.M,F1474.M,F1481.M,F1482.M,F1483.M,F1484.M,F14101.M,F14102.M

Research Interests in Applied Mathematics

 

singular perturbation methods

ordinary and partial differential equations

matched asymptotic expansions

boundary layers

multiple scales

averaging

nonlinear dynamical systems

slow transitions

bifurcations

subharmonic resonances

homoclinic orbits

chaos

nonlinear wave motion

shocks

solitons

dispersive waves

multiphase waves

caustics

mathematical models

fluid dynamics

traffic flow

reaction-diffusion

hydrodynamic stability

critical layers

defects in fiber optics

B.S. in Applied Mathematics, M.I.T., June 1967

Ph.D. in Applied Mathematics, M.I.T., September 1971

 

 

Professional Experience

 

Southern Methodist University

Professor of Mathematics (1985-present), Associate Professor (1978-1985)

The Ohio State University (1977-1978)

Assistant Professor of Mathematics

Rutgers University (1972-1977)

Assistant Professor of Mathematics

University of California, San Diego (1971-1972)

Post-doctoral research, Institute of Geophysics and Planetary Physics

Lecturer, Department of Applied Mechanics and Engineering Sciences

1.     "Critical layers in parallel flows," Studies in Applied Math. 51 (1972), pp. 139-161.

 

2.     "Note on slightly unstable nonlinear wave systems," J. of Fluid Mechanics 58 (1973), pp. 129-142.

 

3.     "Wave induced distortions of a slightly stratified shear flow - a nonlinear critical layer effect,"

        Journal of Fluid Mechanics 58 (1973), pp. 727-735.

 

4.     "Nonlinear perturbations of the Orr-Sommerfeld equation - asymptotic expansion of the logarithmic phase shift across

        the critical layer," SIAM J. Math. Analysis 7 (1976), pp. 70-81.

 

5.     "Resonantly coupled nonlinear evolution equations," (with M. J. Ablowitz), Math. Phys. 16 (1975), pp. 2301-2305.

 

6.     "Some higher order nonlinear evolution equations," Studies in Applied Math. 54 (1975), pp. 275-282.

 

7.     "Note on generating nonlinear evolution equations," SIAM J. Applied Math. 31 (1976), pp. 47-51.

 

8.     "Nonlinear evolution equations - two and three dimensions," (with M. J. Ablowitz),

         Physical Review Letters 35 (1975), pp. 1185-1188.

 

9.     "On the singular behavior of spatially dependent nonlinear wave envelopes,"

        SIAM J. Applied Math. 32 (1977), pp. 154-163.

 

10.     "An infinite number of conservation laws for coupled nonlinear evolution equations,"

         J. Math. Phys. 18 (1977), pp. 1137-1139.

 

11.     "Nonlinear transition layers - the second Painleve transcendent," Studies in Applied Math. 57 (1977), pp. 247-270.

 

12.     "Slowly varying jump and transition phenomena associated with algebraic bifurcation problems,"

        SIAM J. Applied Math. 37 (1979), pp. 69-106.

 

13.     "Energy bounds for the slow capture by a center in sustained resonance,"

        SIAM J. Applied Math. 43 (1983), pp. 244-256.

 

14.     "Nonlinear cusped caustics for dispersive waves," (with Ren-ji Sun), Studies in Applied Math. 72 (1985), pp. 1-37.

 

15.     "Slowly varying solitary wave tails: Focusing, cusped caustics, wave number shocks and birth of tails,"

        (with D. Allgaier), SIAM J. Applied Math. 45 (1985), pp. 919-927.

 

16.     "Note on the initial formation of shocks," SIAM J. Applied Math. 46 (1986), pp. 16-19.

 

17.     "The initial formation and structure of two-dimensional diffusive shock waves," Wave Motion 8 (1986), pp. 267-276.

 

18.     "The modulated phase shift for strongly nonlinear, slowly varying, and weakly damped oscillators,"

        (with F. J. Bourland), SIAM J. Applied Math. 48 (1988), pp. 737-748.

 

19.     "Variation of wave action: modulations of the phase shift for strongly nonlinear dispersive waves with weak

        dissipation," (with F. J. Bourland), Physica 32D (1988), pp. 72-82.

 

20.     "The modulated phase shift for weakly dissipated nonlinear oscillatory waves of the Korteweg-deVries type,"

        Studies in Applied Math. 78 (1988), pp. 73-90.

 

21.    "The slowly varying phase shift for perturbed, single and multi-phased, strongly nonlinear, dispersive waves,"

        (with F. J. Bourland), Physica 35D (1989), pp. 127-147.

 

22.     "Wave number shocks for the leading tail of Korteweg-deVries solitary waves in slowly varying media,"

        (with D. Allgaier), Wave Motion 12 (1990), pp. 569-581.

 

23.     "Separatrix crossing: time-invariant potentials with dissipation", (with F. J. Bourland),

        SIAM J. Applied Math. 50 (1990), pp. 1716-1744.

 

24.     "Averaging method for the phase shift of arbitrarily perturbed strongly nonlinear oscillators with an application to

        capture", (with F. J. Bourland and W. L. Kath), SIAM J. Applied Math. 51 (1991), pp. 1150-1167.

 

25.     "Phase shift modulations for stable, oscillatory, traveling, strongly nonlinear waves",

        Studies in Applied Math. 84 (1991), pp. 57-69.

 

26.     "Standard form and a method of averaging for strongly nonlinear oscillatory dispersive traveling waves",

        SIAM J. Applied Math. 51 (1991), pp. 1638-1652.

 

27.     "The accommodation of traveling waves of Fisher's type to the dynamics of the leading tail",

        (with M. R. Booty and A. A. Minzoni), SIAM J. Applied Math. 53 (1993), pp. 1009-1025.

 

28.     "Connection across a separatrix with dissipation", (with F. J. Bourland),

        Studies in Applied Math. 91 (1994), pp. 95-124.

 

29.     "Higher-order change of the Hamiltonian (energy) for nearly homoclinic orbits", (with E. K. Ho),

        Meth. Appl. Anal. 1 (1994), pp. 446-464.

 

30.     "Boundary of the basin of attraction for weakly damped primary resonance", (with E. K. Ho),

        ASME J. Applied Mech. 62 (1995), pp. 941-946.

 

31.     "Logarithmic correction to the probability of capture for dissipatively perturbed Hamiltonian systems", (with E. K. Ho),

        Chaos 5 (1995), pp. 374-384.

 

32.     "Higher-order change of the Hamiltonian between saddle approaches by phase plane matching", (with E. K. Ho),

         Int. J. Non-Linear Mech. 31 (1996), pp. 239-254.

 

33.     "Accurate phase after slow passage through subharmonic resonance", (with J. D. Brothers),

        SIAM J. Appl. Math. 59 (1998), pp. 347-364.

 

34.     "Slow passage through a homoclinic orbit with subharmonic resonances", (with J. D. Brothers),

        Studies in Applied Math. 101 (1998), pp. 211-232.

 

35.     "Resonant capture and separatrix crossing in dual-spin spacecraft", (with R. Rand and T. Yuster),

        Nonlinear Dynamics 18 (1999), pp. 159-184.

 

36.     "Sequences of orbits and the boundaries of the basin of attraction for two double heteroclinic orbits", (with R. Rand),

        Int. J. Non-Linear Mech. 34 (1999), pp. 1047-1059.

 

37.     "Slow passage through a saddle-center bifurcation", (with D. C. Diminnie),

        J. Nonlinear Science 10 (2000), pp. 197-221.

 

38.     "Weakly nonlinear long waves in channel flow with internal dissipation", (with J. Yu and J. Kevorkian),

        Studies in Applied Math. 105 (2000), pp. 143-163.

 

39.     "Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a

        nonhyperbolic homoclinic orbit", Chaos 10 (2000), pp. 641-648.

 

40.     "Slow passage through the nonhyperbolic homoclinic orbit associated with a subcritical pitchfork bifurcation for

        Hamiltonian systems and the change in action", SIAM J. Appl. Math 62 (2001), pp. 488-513.

 

41.     "Slow passage through the nonhyperbolic homoclinic orbit of the saddle-center Hamiltonian bifurcation",

        (with D.C. Diminnie) Studies in Applied Math. 108 (2002), pp. 65-75.

 

42.     "Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in adiabatic

        invariant", (with D.C. Diminnie) Physica D 162 (2002), pp. 34-52.

 

43.     "Action and period of homoclinic and periodic orbits for the unfolding of a saddle-center bifurcation",

        (with D.C. Diminnie) Int. J. Bifurcation and Chaos 13 (2003), pp. 3519-3530.

 

44.     "Interaction of sine-Gordon kinks with defects: The two-bounce resonance", (with Roy H. Goodman)

        Physica D  (submitted).

 

1.     Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow An Introduction to Applied

        Mathematics, Prentice-Hall, Englewood Cliffs, N.J., 1977, 402 pages. Also Japanese translation.

        Reprinted SIAM Classic Series #21, 1998.

 

2.     Applied Partial Differential Equations (with Fourier Series and Boundary Value Problems), Prentice-Hall,

        Upper Saddle River, N.J., 1983, 1987, 1998 (Fourth Edition, 2004, 759 pages).

        Also Instructor's Manual. Also Spanish translation.

 

3.     Introduction to Differential Equations with Boundary Value Problems (with Stephen L. Campbell), Houghton-Mifflin,

        Boston, 1996, 729 pages. Also Instructor's Manual. Also Spanish translation.

1.     "Energy bounds for the slow capture by a center," Trends in Theory and Practice of Nonlinear Differential Equations,

        ed. V. Lakshmikantham, Dekker, New York, 1984, pp. 227-230.

 

2.     "Nonlinear focusing of dispersive waves," (with Ren-ji Sun), Lectures in Applied Mathematics: V. 23 - Part 2

        Nonlinear Systems of Partial Differential Equations in Applied Mathematics,

        ed. B. Nicolaenko, D. D. Holm, and J. M. Hyman, AMS, Providence, 1986, pp. 67-78.

 

3.     "Phase shift for strongly nonlinear slowly varying oscillators with perturbations", (with F. J. Bourland),

         BAIL V Conf. Proc., Boole Press, Dublin, 1988, pp. 92-97.

 

4.     "Focusing at a nonlinear penumbral caustic", (with Ren-ji Sun), BAIL V Conf. Proc., Boole Press, Dublin, 1988,

        pp. 339-344.

 

5.     "Capture and the connection formulas for the transition across a separatrix", (with F. J. Bourland), Asymptotic Analysis

        and the Numerical Solution of Partial Differential Equations,

        ed. H. G. Kaper and M. Garbey, Dekker, New York, 1991, pp. 17-30.

 

6.     "Phase shift modulations for perturbed strongly nonlinear oscillatory dispersive waves", Nonlinear Dispersive Wave

         Systems, ed. L. Debnath, World Sci., Singapore, 1992, pp. 73-82.

 

7.     "Matching across subharmonic resonance", (with J. D. Brothers), ICIAM 95 Conf. Proc. in ZAMM 76 (1996)

        pp. 489.

 

8.     "On the dynamic unfolding of a saddle-center bifurcation and the change in the action", (with D. C. Diminnie),

        Proc. Steklov Inst. Math  (2003) pp. S91-S97. 

        Translated from Trudy Instituta Mathematiki i Mekhaniki UrO RAN (2003)..

 

1.     Ren-ji Sun (Ph.D., SMU, 1984) Thesis entitled "Caustics for dispersive waves: asymptotics of nonlinear Schrodinger

        equation and its Riemann-Hilbert problems".

 

2.     Darrell Allgaier (Ph.D., SMU, 1986) Thesis entitled "Wave number shocks for the tail of Korteweg-deVries solitary

        waves in slowly varying media".

 

3.     F. Jay Bourland (Ph.D., SMU, 1989) Thesis entitled "Modulations of the phase shift for nonlinear oscillators and

        dispersive waves and connections across a separatrix".

 

4.     Eric K. Ho (Ph.D., SMU, 1993) Thesis entitled "Hamiltonian systems with dissipation: basins of attraction and nearly

        homoclinic orbits".

 

5.     Jerry D. Brothers (Ph.D., SMU, 1995) Thesis entitled "Sequence of subharmonic resonances

        and slow separatrix crossing".

 

6.     David C. Diminnie (Ph.D., SMU, 2000) Thesis entitled "Slow passage through homoclinic orbits associated with the

        unfolding of a saddle-center bifurcation"

 

The contents of this home page are the sole responsibility of Professor Haberman and its contributors, and do not necessarily represent the opinions or policies of Southern Methodist University. The administrator of this page is Professor Haberman, who may be contacted at: rhaberma@mail.smu.edu

Last revision: January 27, 2004.