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Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics. (English) Zbl 0997.35063

Summary: This review paper gives an extensive overview of the soliton solutions for some famous partial differential equations like KdV, mKdV, Sine-Gordon, and nonlinear Schrödinger equations. Different analytical methods of treatment as well as those of numerical methods are presented. Finally, relations between the soliton solution and fluid mechanics are shown.

MSC:

35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
76B25 Solitary waves for incompressible inviscid fluids
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