scholarly journals Symbolic computation of conservation laws of nonlinear partial differential equations in multi-dimensions

2005 ◽  
Vol 106 (1) ◽  
pp. 278-299 ◽  
Author(s):  
Willy Hereman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Symbolic Computation ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential

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

Open Physics ◽  
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.

scholarly journals Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 164-169
Author(s):  
Maysaa Mohamed Al Qurashi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Nonlinear Partial Differential Equations ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Systems Of Pdes ◽  
First Time ◽  
Conservation Theorem

AbstractIn this paper, we examine conservation laws (Cls) with conformable derivative for certain nonlinear partial differential equations (PDEs). The new conservation theorem is used to the construction of nonlocal Cls for the governing systems of equation. It is worth noting that this paper introduces for the first time, to our knowledge, the analysis for Cls to systems of PDEs with a conformable derivative.

New types of interaction solutions to the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

2020 ◽  
Vol 34 (23) ◽  
pp. 2050237
Author(s):  
Yuexing Bai ◽  
Temuerchaolu ◽  
Yan Li ◽  
Sudao Bilige
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Nonlinear Partial Differential Equations ◽  
Lump Solution ◽  
Biological Engineering ◽  
Partial Differential ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Petviashvili Equation

In this paper, with the aid of symbolic computation system Maple, and based on the simplified Hirota method and ansatz technique, we discussed the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation with [Formula: see text] to obtain lump solutions, lump–kink solutions and three classes of interaction solutions. Comparing our new results with other researchers’ results shows that using this method gives the more opportunity to solve the nonlinear partial differential equations that appear in mathematics, physics, biological engineering and other fields. We also presented profiles of new lump solution, lump–kink solutions and interaction solutions as illustrative examples.

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