scholarly journals Numerical solution for the (2+1) dimensional Sobolev and regularized long wave equations arise in fluid mechanics via wavelet technique

2021 ◽  
Vol 3 ◽  
pp. 100016
Author(s):  
Kumbinarasaiah S.
Keyword(s):  
Fluid Mechanics ◽  
Numerical Solution ◽  
Wave Equations ◽  
Long Wave ◽  
Wavelet Technique

The Generalisation of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

1997 ◽  
Vol 66 (5) ◽  
pp. 1288-1290 ◽  
Author(s):  
Thangavel Alagesan ◽  
Ambigapathy Uthayakumar ◽  
Kuppusamy Porsezian
Keyword(s):  
Wave Equations ◽  
Long Wave

Symmetry Reduction, Exact Solutions, and Conservation Laws of the (2+1)-Dimensional Dispersive Long Wave Equations

2009 ◽  
Vol 64 (9-10) ◽  
pp. 597-603 ◽  
Author(s):  
Zhong Zhou Dong ◽  
Yong Chen
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Symmetry Group ◽  
Infinite Number ◽  
Wave Equations ◽  
Direct Method ◽  
Discrete Groups ◽  
Point Symmetry Group ◽  
Long Wave ◽  
Full Symmetry

By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D. Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

scholarly journals Variational theory for (2+1)-dimensional fractional dispersive long wave equations

2021 ◽  
pp. 23-23
Author(s):  
Xiao-Qun Cao ◽  
Cheng-Zhuo Zhang ◽  
Shi-Cheng Hou ◽  
Ya-Nan Guo ◽  
Ke-Cheng Peng
Keyword(s):  
Porous Media ◽  
Nonlinear Waves ◽  
Inverse Method ◽  
Wave Equations ◽  
Continuous Medium ◽  
Variational Principles ◽  
Variational Theory ◽  
Long Wave ◽  
Potential Applications ◽  
Fractional System

This paper extends the (2+1)-dimensional Eckhaus-type dispersive long wave equations in continuous medium to their fractional partner, which is a model of nonlinear waves in fractal porous media. The derivation is shown briefly using He?s fractional derivative. Using the semi-inverse method, the variational principles are established for the fractional system, which up to now are not discovered. The obtained fractal variational principles are proved correct by minimizing the functionals with the calculus of variations, and might find potential applications in numerical modelling.

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