Integration of the loaded MKDV equation with a source in the class of rapidly decreasing functions. (Russian. English summary) Zbl 1537.35314
Summary: We consider the Cauchy problem for a loaded modified Korteweg-de Vries equation with a self-consistent source. The evolution of the scattering data of the Dirac operator, whose potential is a solution of the loaded modified Korteweg-de Vries equation with a self-consistent source in the class of rapidly decreasing functions, is derived. A specific example is given to illustrate the application of the obtained results.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 35P25 | Scattering theory for PDEs |
Keywords:
loaded modified Korteweg-de Vries equation; self-consistent source; Jost solutions; scattering dataReferences:
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