Related papers: Lump chains in the KP-I equation
Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations…
The Camassa-Holm-Kadomtsev-Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa-Holm equation (CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse…
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar…
A numerical analysis to the scalar form-factor in the $\pi\pi$ and KK coupled--channel system is made by solving the coupled-channel dispersive integral equations, using the iteration method. The solutions are found not unique. Physical…
We consider a class of fully-nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order $\alpha >1$. This class of systems incorporates a classical Hertzian model…
The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Special cases include the integrable KP…
Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is…
Real and regular soliton solutions of the KP hierarchy have been classified in terms of the totally nonnegative (TNN) Grassmannians. These solitons are referred to as KP solitons, and they are expressed as singular (tropical) limits of…
Orthogonal and symplectic matrix integrals are investigated. It is shown that the matrix integrals can be considered as a $\tau$-function of the coupled KP hierarchy, whose solution can be expressed in terms of pfaffians.
Using the matrix-resolvent method and a formula of the second-named author on the $n$-point function for a KP tau-function, we show that the tau-function of an arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We then…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
A Jimbo-Miwa like nonlinear differential equation in (3+1)-dimensions is developed through a generalized bilinear equation with the generalized bilinear derivatives. Based on the generalized bilinear forms, two classes of lump solutions,…
For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides…
The theme of the first two sections, is to prepare the framework of how from a "complicated" family of index models I in K_1 we build many and/or complicated structures in a class K_2. The index models are characteristically linear orders,…
A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite…
We consider a scalar Fermi-Pasta-Ulam (FPU) system on a square 2D lattice. The Kadomtsev-Petviashvili (KP-II) equation can be derived by means of multiple scale expansions to describe unidirectional long waves of small amplitude with slowly…
In the tropical limit of matrix KP-II solitons, their support at fixed time is a planar graph with "polarizations" attached to its linear parts. In this work we explore a subclass of soliton solutions whose tropical limit graph has the form…
The genus-1 KP-Whitham system is derived for both variants of the Kadomtsev-Petviashvili (KP) equation (namely, the KPI and KPII equations). The basic properties of the KP-Whitham system, including symmetries, exact reductions, and its…