A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources

Abstract

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generalized Darboux transformation with arbitrary functions in time $t$ for the mKPESCS which, in contrast with the Darboux transformation for the mKP equation, provides a non-auto-Bäcklund transformation between two mKPESCSs with different degrees. The formula for $n$-times repeated generalized Darboux transformation is proposed and enables us to find the rational solutions (including the lump solutions), soliton solutions and the solutions of breather type of the mKPESCS.

23 pages, no figures. to appeare in Physica A

References in corpus (5)

• Two binary Darboux transformations for the KdV hierarchy with self-consistent sources
• Generalized Darboux transformations for the KP equation with self-consistent sources
• Negaton and Positon solutions of the soliton equation with self-consistent sources
• On the constrained KP hierarchy
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• Bäcklund transformations for the KP and mKP hierarchies with self-consistent sources
• The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources
• The constrained dispersionless mKP hierarchy and the dispersionless mKP hierarchy with self-consistent sources
• Single-Source Nets of Algebraically-Quantized Reflective Liouville Potentials on the Line I. Almost-Everywhere Holomorphic Solutions of Rational Canonical Sturm-Liouville Equations with Second-Order Poles
• Soliton Equations with Self-Consistent Sources