Solutions of Integrable PDEs: Solving, Properties and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".
Deadline for manuscript submissions: 30 November 2024 | Viewed by 940
Special Issue Editors
Interests: mathematical analysis; partial differential equations; fractional calculus
Interests: linear systems; signals and in computational geometry (cells, paths, cycles); proximity (closeness of fixed sets); algebraic topology (free group & homotopy theory); physics (vector fields)
Special Issue Information
Dear Colleagues,
Integrable PDEs (partial differential equations) are a special class of PDEs that can be solved exactly, meaning that an explicit expression for the solution can be obtained. This contrasts with non-integrable PDEs, where exact solutions are generally not possible, and numerical methods must be used.
Integrable PDEs have been studied extensively over the past several decades, and many powerful mathematical methods have been developed for their analysis. These methods include the inverse scattering transform, the inverse spectral method (including Riemann–Hilbert problems), the method of dressing transformations, the Painlevé test, and the Lax pair method.
Integrable PDEs have important applications in many areas of science and engineering, including fluid mechanics, quantum field theory, nonlinear optics, and soliton theory. Some examples of integrable PDEs include the Korteweg–de Vries equation, the nonlinear Schrödinger equation, and the sine-Gordon equation. The study of integrable PDEs has led to many important insights into the nature of nonlinear phenomena and has opened up new avenues for research in a wide range of fields.
Dr. Hayman Thabet
Prof. Dr. James F Peters
Prof. Dr. Subhash Kendre
Guest Editors
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Keywords
- integrable PDEs including: Korteweg–de Vries equation
- nonlinear Schrödinger equation
- Sine-Gordon equation
- Boussinesq equation
- Kadomtsev–Petviashvili equation
- mathematical methods for solving the integrable PDEs include: inverse scattering transform
- Riemann–Hilbert problem
- Lax pair method
- inverse spectral method
