The new integrable deformations of short pulse equation and sine-Gordon equation, and their solutions

Details The new integrable deformations of short pulse equation and sine-Gordon equation, and their solutions The new integrable deformations of short pulse equation and sine-Gordon equation, and their solutions

2010-12-02

arxiv.org/abs/1012.0462v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, to appear in J. Phys. A: Math. Theor

Scientific paper

We first derive an integrable deformed hierarchy of short pulse equation and their Lax representation. Then we concentrated on the solution of integrable deformed short pulse equation (IDSPE). By proposing a generalized reciprocal transformation, we find a new integrable deformed sine-Gordon equation (IDSGE) and its Lax representation. The multisoliton solutions, negaton solutions and positon solutions for the IDSGE and the N-loop soliton solutions, N-negaton and N-positon solutions for the IDSPE are presented. In the reduced case the new N-positon solutions and N-negaton solutions for short pulse equation are obtained.

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