Long-time asymptotics for the Nonlocal mKdV equation

29 Apr 2018 He Fengjing Fan Engui Xu Jian

In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_x(x,t)=0,\] which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation... (read more)

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  • EXACTLY SOLVABLE AND INTEGRABLE SYSTEMS