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A study of nonlinear dispersive equations with solitary-wave solutions having compact support. (English) Zbl 0999.65109
The nonlinear \(K(m,n)\) equation \(u_{t} + (u^{m})_{x} +(u^{n})_{xxx} = 0\) and its exact solution by the Adomian decomposition method are discussed. Then two numerical illustrations \(K(2,2)\) and \(K(3,3)\) are investigated to illustrate the pertinent features of the proposed scheme. The technique can be used for any nonlinear dispersive equations.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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