A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear
equations, with an aim to construct a specific sub-class of N-soliton solutions formed by …

We explore the dynamical properties of transformed nonlinear waves (TNWs) for the (3+ 1)-
dimensional B-type Kadomtsev–Petviashvili (BKP) equation describing the propagation of …

We reveal the origin and structure of self-consistent source extensions of integrable
equations from the perspective of binary Darboux transformations. They arise via a …

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 …

Abstract An extended Harry Dym hierarchy is constructed by using eigenfunctions and
adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with …

Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a
q-deformed mKP hierarchy with self-consistent sources (q-mKPHSCSs) is constructed. The …

Inspired by the squared eigenfunction symmetry constraint, we introduce a new τ k-flow
by'extending'a specific t n-flow of a discrete KP hierarchy (DKPH). We construct an extended …

A method is proposed in this paper to construct a new extended q-deformed KP (q-KP)
hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of …

Topological 1-soliton solution of Kadomtsev–Petviashvili equation with power law nonlinearity -
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We show that the discrete Kadomtsev–Petviashvili (KP) equation with sources obtained
recently by the “source generalization” method can be incorporated into the squared …