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Register a new userExact solutions for the Generalized Modified Degasperis-Procesi equation
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Added by
Alvaro Salas Humberto
Publication date
2008
fields
Physics
and research's language is
English
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this paper we show some new exact solutions for the generalized modified Degasperis$-$Procesi equation (mDP equation)
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In this paper we show some new exact solutions for the generalized modified Degasperis$-$Procesi equation (mDP equation)
In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different parametric regimes and (ii) a loop soliton with a conventional soliton in detail.
The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa-Holm equation. In this paper, we study the orbital stability problem of the peaked solitons to the Degasperis-Procesi equation on the line. By constructing a Liapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations.
We present the fundamental solutions for the spin-1/2 fields propagating in the spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.
In this paper we show some exact solutions for the general fifth order KdV equation. These solutions are obtained by the extended tanh method.
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