Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

Rational Wave Solutions and Dynamics Properties of the Generalized ( 2 + 1 )-Dimensional Calogero-Bogoyavlenskii-Schiff Equation by Using Bilinear Method

“…By using a transformation of the potential function of NLEEs and the definition and properties of the D operator, NLEEs are written in bilinear form, and then, the single-double-multiple soliton solutions of NLEEs can be obtained by using the small parameter expansion method. Based on these methods, one can try to find many interesting analytical solutions of NLEEs, such as the rogue wave solutions [2][3][4], the multiple wave solutions [5,6], the lump solutions [7][8][9], the periodic wave solutions [10][11][12][13], the Wronskian solutions [14,15], the rational solutions [16,17], the high-order soliton solutions [18,19], the solitary wave solutions [20,21], and the other solutions [22][23][24][25][26][27].…”

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

“…Up to days, many techniques have been introduced for deriving exact wave solutions of nonlinear models but the innovation reached is deficient. The precise mathematical methods to derive different classes of exact solutions namely; the inverse variational methods [1], the Darboux Transformation [2], the Exp-function technique [3], tanh method [4], the exp(-(Φ)η)-expansion method [5], first integral scheme [6], the tan(Θ/2)-expansion approach [7], the Hirota bilinear method [8][9], the sine-cosine analysis [10], the new extended (G'/ G)-expansion method [11], the modified double sub-equation method [12], the mapping and ansatz methods [13][14], the Jacobi elliptic function expansion method [15][16] as well.…”

Multi-soliton, breathers, lumps and interaction solution to the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation

“…The explicit solutions of NLEEs play a prominent role in the study of nonlinear science. Various effective procedure have been developed to solve NLEEs, like the inverse scattering transform [1], the Darboux transformation [2], Backlund transformation [3], the unified method (UM) and its generalized form (GUM) [4, 5] and Hirota bilinear form method [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. The Hirota's bilinear method is one of the most direct and convenient method to obtain the exact soliton solution of NLEEs.…”

“…Recently, researchers are highly impressed to rogue wave solutions [9, 10] for it's engrossing class of lump-type solutions, which can be found in plasma, shallow-water waves, nonlinear optics and Bose-Einstein condensates [11]. In 2002, Lou et al.…”