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 and the generalized nonlinear Schrödinger equation with nonlinear dispersion GNLS. Taking advantage of the new subsidiary ODE, this F-function method is used to map the solutions of and GNLS equations to those of that nonlinear ODE. As result, we can successfully obtain in a unified way, many exact solutions.
|81Q05||Closed and approximate solutions to quantum-mechanical equations|
|35Q55||NLS-like (nonlinear Schrödinger) equations|
|76D33||Waves in incompressible viscous fluids|
|35Q35||PDEs in connection with fluid mechanics|