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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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