scholarly journals Nonlinear differential equations: Lie symmetries, conservation laws and other approaches of solving

2020 ◽  
Vol 13 (10) ◽  
pp. i-ii
Author(s):  
Chaudry Masood Khalique ◽  
◽  
Muhammad Usman ◽  
Maria Luz Gandarais ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Nonlinear Differential Equations ◽  
Lie Symmetries

Symmetries and conservation laws of a damped Boussinesq equation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640012 ◽  
Author(s):  
María Luz Gandarias ◽  
María Rosa
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Source Term ◽  
Boussinesq Equation ◽  
Lie Symmetries ◽  
Multiplier Method ◽  
Independent Source ◽  
Damped Equation

In this work, we consider a damped equation with a time-independent source term. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. We also present some exact solutions. Conservation laws for this equation are constructed by using the multiplier method.

scholarly journals Equations with an infinite number of explicit conservation laws

1997 ◽  
Vol 127 (1) ◽  
pp. 11-19
Author(s):  
D. B. Fairlie
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Infinite Number ◽  
Nonlinear Differential Equations ◽  
Two Dimensions ◽  
Homogeneous Polynomials ◽  
Charge Densities ◽  
First Order ◽  
Independent Variables ◽  
Infinite Set

A large class of first-order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved charge densities are all homogeneous polynomials in the unknown functions which satisfy the differential equations in question. The simplest member of the class of equations is related to the Born–Infeld Equation in two dimensions. It is observed that some members of this class possess identical charge densities. This enables the construction of a set of multivariable equations with an infinite number of conservation laws.

scholarly journals Approximate Noether Symmetries of Perturbed Lagrangians and Approximate Conservation Laws

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2900
Author(s):  
Matteo Gorgone ◽  
Francesco Oliveri
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Variational Problems ◽  
Lie Symmetries ◽  
Noether Symmetries ◽  
Noether Theorem ◽  
Symmetries Of Differential Equations ◽  
Approximate Lie Symmetries ◽  
Consistent Approach

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we state an approximate Noether theorem leading to the construction of approximate conservation laws. Some illustrative applications are presented.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

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