NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ON HOMOGENEOUS SPACES

The work of A.K.N.S. which is based on the sl(2, R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations. This is achieved by assuming the soliton connection having values in a simple Lie, Kac-Moody, Lie superalgebras. Extensions of some of the integrable nonlinear partial differential equations are given explicitly. In particular the coupled NLS equations on various homogeneous spaces and the coupled modified KdV integro-differential equations are obtained on symmetric spaces.

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NONLINEAR SCHRÖDINGER EQUATIONS ON SUPER SYMMETRIC SPACES RELATED TO LIE SUPERALGEBRAS A(m, n)

International Journal of Modern Physics A ◽

10.1142/s0217751x91002197 ◽

1991 ◽

Vol 06 (26) ◽

pp. 4655-4666 ◽

Cited By ~ 1

Author(s):

AHMET CANOḠLU ◽

BAHRİ GÜLDOḠAN ◽

SELÂMİ SALİHOḠLU

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Symmetric Spaces ◽

Nonlinear Partial Differential Equations ◽

Lie Superalgebras ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

We obtain new integrable coupled nonlinear partial differential equations by assuming that the soliton connection has values in the Lie superalgebras A(m, n). These equations are coupled nonlinear Schrödinger equations on various super symmetric spaces.

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NONLINEAR SCHRÖDINGER EQUATIONS ON SUPER SYMMETRIC SPACES RELATED TO ORTHOGONAL-SYMPLECTIC LIE SUPERALGEBRAS

International Journal of Modern Physics A ◽

10.1142/s0217751x92003343 ◽

1992 ◽

Vol 07 (29) ◽

pp. 7287-7304 ◽

Cited By ~ 1

Author(s):

AHMET CANOGLU ◽

BAHRI GÜLDOGAN ◽

SELÂMI SALIHOGLU

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Symmetric Spaces ◽

Nonlinear Partial Differential Equations ◽

Lie Superalgebras ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

We obtain new integrable coupled nonlinear partial differential equations by assuming the soliton connection having values in orthogonal-symplectic Lie superalgebras [B(m, n), C(n), D(m, n)]. These equations are coupled Nonlinear Schrödinger equations on various super symmetric spaces.

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Nonlinear Partial Differential Equations and Related Problems of Pade Approximations.

10.21236/ada141519 ◽

1983 ◽

Author(s):

D. V. Chudnovsky ◽

G. V. Chudnovsky

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Padé Approximations ◽

Partial Differential ◽

Pade Approximations

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Numerical and Analytical Methods in Nonlinear Partial Differential Equations.

10.21236/ada185210 ◽

1987 ◽

Author(s):

Richard E. Ewing

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Analytical Methods ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

Numerical And Analytical Methods

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Formation of Shocks for Nonlinear Partial Differential Equations of First Order

Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–22 August 1993 ◽

10.1515/9783112318874-022 ◽

1994 ◽

pp. 199-204

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

First Order

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Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

Forum Mathematicum ◽

10.1515/forum-2020-0232 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Robert Stegliński

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Nonlinear Partial Differential Equations ◽

Dirichlet Boundary Conditions ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Lyapunov Inequalities ◽

Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

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Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽

10.1515/phys-2020-0163 ◽

2020 ◽

Vol 18 (1) ◽

pp. 545-554

Author(s):

Asghar Ali ◽

Aly R. Seadawy ◽

Dumitru Baleanu

Keyword(s):

Wave Propagation ◽

Partial Differential Equations ◽

Differential Equations ◽

Longitudinal Wave ◽

Symbolic Computation ◽

Boussinesq Equation ◽

Nonlinear Partial Differential Equations ◽

Wave Model ◽

Simple Equation ◽

Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

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