A Generalized Dressing Approach for Solving the Extended KP and the Extended mKP Hierarchy

Abstract

A combination of dressing method and variation of constants as well as a formula for constructing the eigenfunction is used to solve the extended KP hierarchy, which is a hierarchy with one more series of time-flow and based on the symmetry constaint of KP hierarchy. Similarly, extended mKP hierarchy is formulated and its zero curvature form, Lax representation and reductions are presented. Via gauge transformation, it is easy to transform dressing solutions of extended KP hierarchy to the solutions of extended mKP hierarchy. Wronskian solutions of extended KP and extended mKP hierarchies are constructed explicitly.

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References in corpus (7)

• The $n$-component KP hierarchy and representation theory
• A new extended KP hierarchy
• A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources
• A new extended q-deformed KP hierarchy
• A New ``Dual'' Symmetry Structure of the KP Hierarchy
• A new multi-component two dimensional Toda lattice hierarchy and two dimensional Toda lattice with self-consistent sources
• Bäcklund transformations for the KP and mKP hierarchies with self-consistent sources

Cited by in corpus (8)

• A new extended discrete KP hierarchy and generalized dressing method
• The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons
• Discrete KP equation with self-consistent sources
• A new extended matrix KP hierarchy and its solutions
• A new $({\gamma }_n,{\sigma }_k)-$ KP hierarchy and generalized dressing method
• Matrix generalizations of integrable systems with Lax integro-differential representations
• A new bidirectional generalization of (2+1)-dimensional matrix k-constrained KP hierarchy
• Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy