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New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations. (English) Zbl 1114.65124
Summary: We establish new solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations. Unlike the standard Degasperis-Procesi and Camassa-Holm equations, where multi-peakon solutions arise, the modified forms cause a change in the characteristic of these solutions and change it to bell-shaped solitons, periodic, and complex solutions. The extended tanh method, the rational hyperbolic functions method, and the rational exponential functions method are employed to reveal these new solutions.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K30 Initial value problems for higher-order parabolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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