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The sub-ODE method for finding exact travelling wave solutions of generalized nonlinear Camassa-Holm, and generalized nonlinear Schrödinger equations. (English) Zbl 1217.81074
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.
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q55NLS-like (nonlinear Schrödinger) equations
76D33Waves in incompressible viscous fluids
35Q35PDEs in connection with fluid mechanics