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Compacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarie’s fractional derivative. (English) Zbl 1255.35218
Summary: In this Letter, the fractional variational iteration method using Heś polynomials is implemented to construct compacton solutions and solitary pattern solutions of nonlinear time-fractional dispersive KdV-type equations involving Jumarie’s modified Riemann-Liouville derivative. The method yields solutions in the forms of convergent series with easily calculable terms. The obtained results show that the considered method is quite effective, promising and convenient for solving fractional nonlinear dispersive equations. It is found that the time-fractional parameter significantly changes the soliton amplitude of the solitary waves.
MSC:
35R11Fractional partial differential equations
35Q53KdV-like (Korteweg-de Vries) equations
35C08Soliton solutions of PDE
35B36Pattern formation in solutions of PDE
39B12Iterative and composite functional equations
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