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In this talk, we present an efficient numerical scheme to calculate the N-periodic wave solutions to the Tzitzeica equation, the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation and the mKdV-...
The talk is about applications of bilinear approaches to N-soliton solutions in (2+1)-dimensions. The Hirota N-soliton condition will be analyzed, together with novel examples of (2+1)-dimensional sol...
We will talk about the Hirota direct method and its applications to soliton solutions in (1+1)-dimensions. Both known and new examples of soliton equations will be discussed, and generalized bilinear ...
We use the theory of Gabor frames to prove the boundedness of bilinear pseudodifferentialoperators on products of modulation spaces. In particular,we show that bilinear pseudodifferential operators co...
This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Le...
A new type of the KP equation with self-consistent sources (KPESCS) 痳st found by Melnikov ( Lett. Math. Phys. 7(1983) 129-136)is re-constructed via source generation procedure. New feature of the ob...
The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's com...
In this paper, we improve a recent result by Li and Peng on products of functions in $H_L^1(\bR^d)$ and $BMO_L(\bR^d)$, where $L=-\Delta+V$ is a Schr\"odinger operator with $V$ satisfying an appropria...
Abstract: We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on a...
The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg spin chain are investigated by means of a low-energy approach and large scale numerical calculations. In sharp contrast to ...
We use Jones-Wenzl idempotents to construct bases for the relative Kauffman bracket skein module of a square with n points colored 1 and one point colored h. We consider a natural bilinear form on thi...
We prove an improved version of bilinear local smoothing estimate to Airy solutions.Using this we study a smoothing property of Duhamel part of nonlinear solutions to the mass-critical generalized Kd...
The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. We provide several onstructions leading t...
We prove that if the Hausdorff dimension of the set E  R2 is greater than 74 , then the three-dimensional Lebesgue measure of the set of triangles determined by E is positive. We establish this fact...

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