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New exact solutions for modified nonlinear dispersive equations \(mK(m,n)\) in higher dimensions spaces. (English) Zbl 1073.35052
Summary: With the use of some proper transformations and symbolic computation, we present a general and unified method for investigating the general modified nonlinear dispersive equations \(mK(m,n)\) in higher dimensions spaces. The work formally shows how to construct the general solutions and some special exact-solutions for \(mK(m,n)\) equations in higher dimensional spatial domains. The general solutions not only contain the solutions by A. M. Wazwaz [Math. Comput. Simul. 59, No. 6, 519–531 (2002; Zbl 0996.35065)] but also contain many new compact and noncompact solutions.

MSC:
35C05 Solutions to PDEs in closed form
35Q53 KdV equations (Korteweg-de Vries equations)
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