The sub-ODE method for finding exact travelling wave solutions of generalized nonlinear Camassa-Holm, and generalized nonlinear Schrödinger equations. (English) Zbl 1217.81074

Yomba, Emmanuel

Phys. Lett., A 372, No. 3, 215-222 (2008).

Summary: With the aid of the ordinary differential equation (ODE) involving an arbitrary positive power of dependent variable proposed by Li and Wang and an indirect F-function method very close to the F-expansion method, we solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection \(C(l,n,p)\) and the generalized nonlinear Schrödinger equation with nonlinear dispersion GNLS\((l,n,p,q)\). Taking advantage of the new subsidiary ODE, this F-function method is used to map the solutions of \(C(l,n,p)\) and GNLS\((l,n,p,q)\) equations to those of that nonlinear ODE. As result, we can successfully obtain in a unified way, many exact solutions.

MSC:

81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55	NLS equations (nonlinear Schrödinger equations)
76D33	Waves for incompressible viscous fluids
35Q35	PDEs in connection with fluid mechanics

Software:

RATH

References:

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