Search
Search Results
-
Parallel Physics-Informed Neural Networks Method with Regularization Strategies for the Forward-Inverse Problems of the Variable Coefficient Modified KdV Equation
This paper mainly introduces the parallel physics-informed neural networks (PPINNs) method with regularization strategies to solve the data-driven...
-
Integrability and Other Analytical Properties of Nonlinear PDE Systems
Integrability of a nonlinear partial differential equation or a system of such equations, in its basic sense, refers to the possibility of...
-
Ultradiscrete hard-spring equation and its phase plane analysis
Ultradiscretization enables us to construct a piecewise linear equation which approximates a given subtraction-free difference equation. Recently...
-
-
Orbital Stability of dn Periodic Wave Solutions of the Boussinesq Equation with Quadratic-Cubic Nonlinear Terms
This paper investigates the problem of the orbital stability of dn periodic wave solutions of the Boussinesq equation with quadratic-cubic nonlinear...
-
Lie Algebra Classification, Conservation Laws and Invariant Solutions for a Generalization of the Sharma–Tasso–Olever Equation
Sharma–Tasso–Olever equation is an interesting partial differential equation with multiple associated studies. This type of nonlinear evolution...
-
Discrete Semiclassical Orthogonal Polynomials of Class 2
In this contribution, discrete semiclassical orthogonal polynomials of class s ≤ 2 are studied. By considering all possible solutions of the Pearson...
-
A Stirling-Type Formula for the Distribution of the Length of Longest Increasing Subsequences
The discrete distribution of the length of longest increasing subsequences in random permutations of n integers is deeply related to random matrix...
-
Kovalevskaya Exponents, Weak Painlevé Property and Integrability for Quasi-homogeneous Differential Systems
We present some necessary conditions for quasi-homogeneous differential systems to be completely integrable via Kovalevskaya exponents. Then, as an...
-
Matrix orthogonal polynomials, non-abelian Toda lattices, and Bäcklund transformations
A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of...
-
Exceptional Orthogonal Polynomials and Rational Solutions to Painlevé Equations
These are the lecture notes for a course on exceptional polynomials taught at the AIMS-Volkswagen Stiftung Workshop on Introduction to Orthogonal...
-
Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many...
-
An Extension to Direct Method of Clarkson and Kruskal and Painlev\(\acute{e}\) Analysis for the System of Variable Coefficient Nonlinear Partial Differential Equations
In this work, direct method of Clarkson and Kruskal has been extended for the system of variable coefficient nonlinear partial differential...
-
Symbolic Computation of Solitary Wave Solutions and Solitons Through Homogenization of Degree
A simplified Hirota method for the computation of solitary waves and solitons of nonlinear partial differential equations (PDEs) is presented. A...
-
On Certain Properties of Perturbed Freud-Type Weight: A Revisit
In this paper, monic polynomials orthogonal with deformation of the Freud-type weight function are considered. These polynomials fulfill linear...
-
-
On the monodromy of the deformed cubic oscillator
We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the...
-
Invariant Manifolds of Hyperbolic Integrable Equations and their Applications
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semidiscrete variant). First, we linearize the equation around...