Multi and breather wave soliton solutions and the linear superposition principle for generalized Hietarinta equation

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

Novel solitary and resonant multi-soliton solutions to the (3 + 1)-dimensional potential-YTSF equation

In this study, the (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation arising from the (3 + 1)-dimensional Kadomtsev–Petviashvili equation is investigated in detail by using two powerful approaches. First, the generalized resonant multi-soliton solution is generated via the simplified linear superposition principle. Second, after applying the simplest equation method, the generalized single solitary solution is extracted. The results show that the obtained solutions are perfect. The physical explanation of the obtained solutions is depicted in various 3D and 2D figures, which are used to illustrate that the interactions of resonant multi-soliton waves are inelastic. Ultimately, the study reveals that the inelastic interactions can be determined by the sign of the wave related number [Formula: see text].

Resonant multi-soliton solutions to two fifth-order KdV equations via the simplified linear superposition principle

In this paper, the simplified linear superposition principle is presented and employed to handle two versions of the fifth-order KdV equations, called the (2[Formula: see text]+[Formula: see text]1)-dimensional Caudrey–Dodd–Gibbon (CDG) equation and the (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation, respectively. Two general forms of resonant multi-soliton solutions are formally obtained. The paper proceeds step-by-step with increasing detail about the derivation process. Firstly, illustrate the algorithms of the linear superposition principle which paves the way for solving the wave related numbers. Then, demonstrate its application that exposes the proposed approach provides enough freedom to construct resonant multi-soliton wave solutions. Finally, some graphical representations of obtained solutions are portrayed by taking some definite values to free parameters, which describe various versions of inelastic interactions of resonant multi-soliton waves. The associated propagations may be related to large variety of real physical phenomena.