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- MATLAB m-files for Figures for Applied Partial Differential Equations Text by Richard Haberman
singular perturbation methods
ordinary and partial differential equations
matched asymptotic expansions
nonlinear dynamical systems
nonlinear wave motion
defects in fiber optics
- Research Interests in Applied Mathematics
- 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),
- 10. "An infinite number of conservation laws for
coupled nonlinear evolution equations,"
- J. Math. Phys. 18 (1977),
- 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),
- 13. "Energy bounds for the slow capture by a center
in sustained resonance,"
- SIAM J. Applied Math. 43 (1983),
- 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),
- 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),
- 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.
- 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.
- J. Nonlinear Science 10 (2000),
- 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
- 2. Applied Partial Differential Equations (with Fourier Series and Boundary Value Problems), Prentice-Hall (now Person),
- Upper Saddle River, N.J., 1983, 1987,
1998, 2004 (Fifth Edition, 2013, 756 pages).
- Also Instructor's Manual. Also
- 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
- 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.
- 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
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Last revision: September 3, 2013.