Blow-up phenomena of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

Generalised Two-Component Modified Weakly Dissipative Dullin-Gottwald-Holm System: Invariance Analysis and Conservation Laws

“…Tian derived asymptotic behaviour [21] and infinite propagation speed [22] of weakly dissipative mDGH2 system. The blow up phenomena of weakly dissipative mDGH2 system has also been derived by Tian et al [23].…”

The sine-Gordon expansion method for higher-dimensional NLEEs and parametric analysis

“…Since the success rate of NLEEs is high in illustrating versatile problems in different sectors, searching solitary wave solutions has gained popularity to the researchers. Thus, a number of methods have been developed by various researchers to carry out exact and explicit stable soliton solutions of nonlinear physical models, such as, the tanh-function expansion and its various modifications [ 4 ], the exp-function method [ 5 ], the ansatz method [ 6 ], the sine-cosine method [ 7 ], the F-expansion method [ 8 ], the complex hyperbolic-function method [ 9 ], the variational iteration method [ 10 ], the -expansion method [ 11 ], the Jacobi elliptic function method [ 12 ], the improved Bernoulli sub-equation function method [ 13 ], the homotopy analysis method [ 14 ], the Adomian decomposition method [ 15 ], the modified extended tanh method [ 16 ], the -expansion method [ 17 ], the finite element method [ 18 ], the first integral method [ 19 ], the alternative expansion method [ 20 ], the modified simple equation method [ 21 ], the modified two-component Dullin-Gottwald-Holm (mDGH2) system [ 22 ], the Riemann-Hilbert method [ 23 , 24 , 25 ], the Lie symmetry method [ 26 ], the long wave limit method [ 27 ], the truncated Painlevé expansion method [ 28 ], the sine-Gordon expansion (SGE) method [ 29 , 30 , 31 , 32 , 33 , 34 ] and several type of soliton [ 35 , 36 ] process. The reputed sine-Gordon equation method was developed based on the wave transformation and it functions only for lower-dimensional NLEEs.…”

A class of localized soliton and fractal pattern solutions of the (2 + 1)-dimensional modified dispersive long wave model

“…The channeling of optical solitons which a tough nonlinear slender film obstacle that can displays jump-like non-adiabatic progress and leads to fission phenomenon has been investigated [7]. In fact, the soliton fission-fusion and annihilation phenomena of various nonlinear models have been derived by the diverse technics such as the Hirota's direct method [8][9][10][11], Backlund transformation [12,13], Blow-up phenomena via direct algebraic approach [14] and the variable separation methods [15]. In addition, the localized excitation solutions to (2+1)-D generalized Sasa-Satsuma model were analyzed via Painlevé analysis [15].…”