Auto-Bäcklund transformation and similarity reductions to the variable coefficients variant Boussinesq system

Auto-Backlund transformations and New Exact Soliton Solutions of KdV Equation for Nonlinear Dust Acoustic Solitary Waves in Dust Plasma with Variable Dust Charge

“…Substituting equations (13)(14)(15)(16)(17) into equations (1-4) and collecting terms with same powers of , from the cofficients of lowest order we have:…”

“…We use the reductive perturbation technique to derive a KdV equation. would like to use the homogeneous balance method [15,16] to construct an auto-Bäcklund transformation (BT) [17][18][19][20][21][22][23] , new exact soliton solutions of KdV equation are obtained and we have applied the modifiedǴ G expansion method [24][25][26][27][28][29][30][31], the sine-cosine expansion method, the sinh-coshine expansion method ,and the sech-tanh expansion method [33,[37][38][39][40][41] and to obtain a new travelling wave solutions of KdV equation. The paper is organized as follows :This introduction in Section 1.…”

Exact Solutions of Space Dependent Korteweg-de Vries Equation by the Extended Unified Method

“…Auto-B a  cklund transformation deals with the exact solutions that were obtained for integrable forms of (2) by truncating Painleve' expansion [3][4][5][6][7][8][9]. Recently auto-B a  cklund transformation that was extrapolated in [10][11][12][13][14] and the homogeneous balance method in [15][16][17][18][19] assert a solution for evolution equations with variable coefficients in the form ), , ( ) ) ( ( = ) , ( …”

Odd-Soliton-Like Solutions for the Variable-Coefficient Variant Boussinesq Model in the Long Gravity Waves

“…Auto-Bäcklund transformation and similarity reductions of System (2) have been derived [18]. Painlevé property for System (2) has been reported under some constraints [19], and the N-solitonic solutions in terms of the Wronskian determinant has been presented by the Hirota technique [19].…”