Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Cot Method

Abstract

Tan-cot

Application of Lie-Group Theory for solving CalogeroBogoyavlenskii- Schiff Equation

“…The detailed description of the method and their applications may be studied in the literature [1-4, [15][16][17][18][19][20] where k i ′ s are arbitrary constants. Therefore, the corresponding Lagrange's system for (2.6) is …”

“…The reduction of variables occurs exploiting the symmetries and using invariance property of the PDE under Lie-group theory. The theory and its applications can be grasped by the researches and text books [15][16][17][18][19][20]. Once the PDE reduces into another PDE with lesser number of independent variable, one can obtain semi analytical/analytical solution of the PDE.…”

Some more similarity solutions of the(2+1)-dimensional BLP system

“…The BLP system and other NLEEs are solved by many efficient methods, notably object reduction approach [8], extended tanh method [9], homotopy analysis and homotopy Padé methods [10], Bifurcation method [11], new mapping method [12], improved projective Riccati equation method [13], Special Painlevé Bäcklund transformations and multilinear variable separation approach [15], modified Clarkson and Kruskal (CK) direct method [16], generalized algebra method [17], tanh-coth method [18], sinh-cosh and sin-cos methods [19] and tan-cot method [20], etc.…”

Resonant Response in Bounded Nonlinear Wave Systems

“…The analytical approach developed and applied in this study, based on perturbation techniques, is one where the leading order solution contains a single mode or multiple modes. It would be interesting to determine the approximate solution by another method like the Tan-Cot method (see Kumar [34] ) and then compare with the analytical solutions found in this thesis. Moreover, to help understand the asymptotic solution with various nonlinearity term (i.e., f (u)) of the model problem discussed in Chapter 3 and 4, we may apply Kevorkian Energy method.…”