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

Helal, M. A.

Chaos Solitons Fractals 13, No. 9, 1917-1929 (2002).

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

Keywords:

review paper; KdV; mKdV; Sine-Gordon; nonlinear Schrödinger equations

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