Related papers: Generalizations of the short pulse equation

We generalize Polya-Szego inequality to integrands depending on $u$ and its gradient. Under minimal additional assumptions, we establish equality cases in this generalized inequality. We also give relevant applications of our study to a…

Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.

We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…

Using the generalized perturbation reduction method the scalar nonlinear Schr\"odinger equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector…

We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.

In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…

The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.

We announce a new bi-Hamiltonian integrable two-component system admitting the scalar 3rd-order Burgers equation as a reduction.

This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.

We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…

The short pulse (SP) equation is a novel model equation describing the propagation of ultra-short optical pulses in nonlinear media. This article reviews some recent results about the SP equation. In particular, we focus our attention on…

We establish derivative estimates of solution of elliptic system in narrow regions.

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained.…

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…

The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…

Multivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.