Related papers: Multi-lump solutions of KP equation with integrabl…
We constructed new classes of exact multi-lump solutions of mKP-1,2 equations with integrable boundary condition $u(x,y,t)\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov. We exactly satisfied reality…
New classes of exact multi-soliton solutions of KP-1 and KP-2 versions of Kadomtsev-Petviashvili equation with integrable boundary condition $u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov are…
We proposed general scheme for construction of exact real periodical solutions of mKP-1 equation via Zakharov-Manakov $\overline{\partial}$-dressing method, derived convenient determinant formula for calculation of such solutions and…
The 2+1-dimensional integrable generalization of Kaup-Kuperschmidt and Sawada-Kotera equations are studied by $\bar\partial$-dressing method of Zakharov and Manakov. The solutions with functional parameters and periodic solutions are…
In this short note we discuss a new formula for solving the nonlocal $\overline{\partial}$-problem, and discuss application to the Manakov--Zakharov dressing method. We then explicitly apply this formula to solving the complex (2+1)D…
A method of looking for boundary conditions consistent with the integrability property of multidimensional Kadomtsev-Petviashvili (KP) type equations is discussed. The method is based on involutions of the Lax pair taken at the border…
The soliton solutions of two different (2+1)-dimensional equations with the third order and second order spatial spectral problems are studied by the $\bar{{\partial}}$-dressing method. The 3-reduced and 5-reduced equations of CKP equation…
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…
In this paper we formulate the nonlocal dbar problem dressing method of Manakov and Zakharov [28, 29, 27] for the 4 scaling classes of the 1+1 dimensional Kaup--Broer system [7, 13]. The method for the 1+1 dimensional Kaup--Broer systems…
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear…
The KP-I equation has family of solutions which decay to zero at space infinity. One of these solutions is the classical lump solution. This is a traveling wave, and the KP-I equation in this case reduces to the Boussinesq equation. In this…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
In this letter, the unique exact lump and topological soliton solutions of integrable (2+1) dimensional Kundu Mukherjee Naskar (KMN) equation are obtained. These solutions have an unusual property that they can get curved in the plane…
The classes of exact multi line soliton, periodic solutions and solutions with functional parameters, with constant asymptotic values at infinity u|_{xi^2+eta^2->infty}->-epsilon, for the hyperbolic and elliptic versions of the…
We propose compact finite difference schemes to solve the KP equations $u\_t + u\_{xxx} + u^p u\_x + $\lambda$ \partial^{--1}\_x u\_{yy} = 0$. When $p = 1$, this equation describes the propagation of small amplitude long waves in shallow…
In this article we derive a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying supported boundary conditions. To this end, we combine the use of a suitable conformal mapping which…
In this note, we show how certain everywhere-regular real rational function solutions of the KP1 equation ("multi-lumps") can be constructed via the polynomial analogs of theta functions from singular rational curves with cusps. We use two…
We prove the continuity of bounded solutions for a wide class of parabolic equations with $(p,q)$-growth $$ u_{t}-{\rm div}\left(g(x,t,|\nabla u|)\,\frac{\nabla u}{|\nabla u|}\right)=0, $$ under the generalized non-logarithmic Zhikov's…