Oblique Traveling Wave Closed-Form Solutions to Space-Time Fractional Coupled Dispersive Long Wave Equation Through the Generalized Exponential Expansion Method

New Wave Solutions for the Two-Mode Caudrey–Dodd–Gibbon Equation

“…Moreover, in order to analyze the dynamical behavior of the novel dual-mode solution (20), the 3D and 2D graphics are presented in Figure 3, considering the particular values of the free parameters as a 2 = 0.1, d = 3, k = 2, α = 0.2, for various values of phase velocity s. Subgraphs (a 1 -a 3 ) present the physical structure of the dual waves G 3 (x, t) and G 4 (x, t) upon increasing s (s = 1, 3, 5), which are, respectively, associated with the values of β = 0.881, 0.971, 0.997. The motion described by (20) looks like singular dual kink waves, as is clearly shown in subgraphs (b 1 -b 3 ), representing the 2D plots of (a 1 -a 3 ) for x = 0. The collision of the waves occurs for the phase velocity s = 5.…”

“…The collision of the waves occurs for the phase velocity s = 5. The influence of parameters k, s, and α on the motion of dual waves (20) is illustrated in subgraphs (a-c) in Figure 4. When increasing both the wave number k within [1,3] and the phase velocity s inside the interval of values s min = 6.8 and s max = 12, we observe that the profiles of G 3 (x, t) and G 4 (x, t) increase and remain fixed for any values k > 3, s > 12.…”

“…In our article, novel dual-mode wave solutions given by ( 19), (20), and ( 24) are generated for arbitrary values of the nonlinearity and dispersion parameters, α and β. To the best of our knowledge, they are reported here for the first time.…”

“…The paper is organized as follows: After the Introduction, in Section 2, an overview on the general form of the TMCDG equation is provided. In Section 3 we present basic facts on the Kudryashov method [18,19] and the exponential expansion method [20]. The findings of our investigation, where the previous methods were applied to the TMCDG equation, are pointed out in Section 4.…”

Constructing and Predicting Solutions for Different Families of Partial Differential Equations: A Reliable Algorithm

“…For more accurate analysis and predictions, it is recommended to use partial diferential equations instead of ordinary diferential equations for modeling various physical phenomena. Tese equations are widely used for describing diferent complex situations, such as fuid fow [3,4], signal processing, control and information theory [5,6], entropy generations [7], and waves on shallow water surfaces [8][9][10]. Examples include radioactive decay, spring-mass systems, population growth, and predator-prey models.…”