Related papers: A Nonstandard Supersymmetric KP Hierarchy
The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
The purpose of this paper is to develop the negative order MKdV hierarchy and to present a new related integrable Neumann-like Hamiltonian flow from the view point of inverse recursion operator and constraint method. The whole MKdV…
We investigate the additional symmetries of several supersymmetric KP hierarchies: the SKP hierarchy of Manin and Radul, the $\hbox{SKP}_2$ hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries…
An extension of the Kadomtsev-Petviashvili (KP) hierarchy defined via scalar pseudo-differential operators was studied in [16, 20]. In this paper, we represent the extended KP hierarchy into the form of bilinear equation of (adjoint)…
Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser system.
An integrable extension of the well known nonlinear Schroedinger (NLS) equation to a higher space-dimension, recently proposed by us, is investigated, exploring its various important aspects. Focusing on the idea of construction its…
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the $UOSp(2\vert 1)$ supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already…
Using a modified WKB approach, we present a rigorous semi-classical analysis for solutions of nonlinear Schroedinger equations with rotational forcing. This yields a rigorous justification for the hydrodynamical system of rotating…
We study a class of planar Schr\"{o}dinger-Poisson systems $$ -\Delta u+\lambda V(x)u+\phi u=f(u) , \quad x\in{\mathbb R}^2,\qquad \Delta \phi=u^2, \quad x\in{\mathbb R}^2, $$ where $\lambda>0$ is a parameter, $V\in C({\mathbb R}^2,{\mathbb…
We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude…
We consider nonlocal linear Schr\"odinger-type critical systems of the type \begin{equation}\label{eqabstr} \Delta^{1/4} v=\Omega\, v~~~\mbox{in $\R\,.$} \ \end{equation} where $\Omega$ is antisymmetric potential in $L^2(\R,so(m))$, $v$ is…
In this paper, we construct the Virasoro type additional symmetries of a kind of constrained multi-component KP hierarchy and give the Virasoro flow equation on eigenfunctions and adjoint eigenfunctions. It can also be seen that the…
We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i} \theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian…
A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr\"odinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass…
We consider the propagation of wave packets for a nonlinear Schr\"odinger equation, with a matrix-valued potential, in the semi-classical limit. For a matrix-valued potential, Strichartz estimates are available under long range assumptions.…
We consider the existence of stationary wave solutions with prescribed mass to a supercritical nonlinear Schr{\"o}dinger equation on a noncompact connected metric graph without a small mass assumption.
The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling…
A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-$N$ limit of…
In this paper, we consider the Cauchy problem for the three dimensional parabolic-elliptic Keller-Segel equation with a large non-shear incompressible flow. Without advection, there exist solution with arbitrarily mass which blow up in…