The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N -coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that the...

In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By analyzing high and low frequency limits of the appropriate periodic Evans function, we derive an orientation index which yields sufficient conditions for such a...

Abstract We show that the configuration in phase space of elliptic Calogero–Moser model when particles stick together pairs is stable under third Hamiltonian flow model. The equations motion for coincide with poles solutions to B-version Kadomtsev–Petviashvili equation.

We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also construction of connections between hydrodynamic optical model fields. Moreover, unlike Kadomtsev–Petviashvili equation (KPE), KP-B allows modeling waves traveling both directions does require zero-mass assumption, is nec...