Periodic solutions of the modified short pulse equation

With the aid of the reciprocal transformation between the modified short pulse (mSP) equation and the sine-Gordon (sG) equation, certain periodic solutions of the mSP equation are constructed. Both one-phase and two-phase periodic solutions are presented. Taking the proper limits of those periodic solutions, various solitary wave solutions such as one-cuspon, two-cuspon and one-breather solutions are recovered. In addition, three novel standing wave solutions for the mSP equation are obtained.

Automated summary

By using the reciprocal transformation between the modified short pulse (mSP) equation and the sine-Gordon (sG) equation, periodic solutions of the mSP equation are constructed and further used to recover solitary wave solutions and novel standing wave solutions. The obtained solutions include one-phase and two-phase periodic solutions, as well as one-cuspon, two-cuspon, and one-breather solutions.