Search
Search Results
-
Bilinear Formalism in Soliton Theory
A brief survey of the bilinear formalism discovered by Hirota is given. First, the procedure to obtain soliton solutions of nonlinear evolution...
-
Nonlinear Waves, Solitons, and IST
These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed...
-
Integrability – and How to Detect It
We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is...
-
Introduction
Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way,...
-
Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: A Review and Extensions of Tests for the Painlevé Property
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity...
-
Lie Bialgebras, Poisson Lie Groups, and Dressing Transformations
In this course, we present an elementary introduction, including the proofs of the main theorems, to the theory of Lie bialgebras and Poisson Lie...
-
Eight Lectures on Integrable Systems
These lectures provide an introduction to the theory of integrable systems from the point of view of Poisson manifolds. In classical mechanics, an...
-
Introduction to the Hirota Bilinear Method
We give an elementary introduction to Hirota’s direct method of constructing multi-soliton solutions to integrable nonlinear evolution equations. We...
-
Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the...
-
Trending on the use of Google mobility data in COVID-19 mathematical models
Google mobility data has been widely used in COVID-19 mathematical modeling to understand disease transmission dynamics. This review examines the...
-
On the study of three-dimensional compressible Navier–Stokes equations
This work is devoted to the study of three-dimensional compressible Navier–Stokes equations on unstructured meshes. The approach used is based on...
-
Global dynamics of a diffusive competitive Lotka–Volterra model with advection term and more general nonlinear boundary condition
We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas,...
-
A modified fuzzy Adomian decomposition method for solving time-fuzzy fractional partial differential equations with initial and boundary conditions
This research article introduces a novel approach based on the fuzzy Adomian decomposition method (FADM) to solve specific time fuzzy fractional...
-
Ψ-Bielecki-type norm inequalities for a generalized Sturm–Liouville–Langevin differential equation involving Ψ-Caputo fractional derivative
The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ -Caputo...
-
Generalized kinetic theory of coarse-grained systems. I. Partial equilibrium and Markov approximations
The general kinetic theory of coarse-grained systems is presented in the abstract formalism of communication theory developed by Shannon and Weaver,...
-
Generalized Tikhonov regularization method for an inverse boundary value problem of the fractional elliptic equation
This research studies the inverse boundary value problem for fractional elliptic equation of Tricomi–Gellerstedt–Keldysh type and obtains a condition...
-
Variance of a strongly additive function defined on random permutations
Inspired by unfading popularity of the Turán–Kubilius inequality for additive number theoretic functions within the last decades, we examine the...