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In this article, the equation showing the cold bosonic atoms in a zig-zag optical lattice model for some breathers, M-shaped solution and lump soliton solution, homoclinic breather pulses, breather lump pulses, periodic-cross kink wave, kink cross-rational propagation, and interaction between lump periodic and kink wave was examined. Some M-shaped solution, M-shaped interaction with periodic and kink, M-shaped interaction with rogue and kink, M-shaped rational solution, M-shaped rational solution with one kink, M-shaped rational solution with two kink, solutions for lump soliton waves, lump one kink waves, lump two kink waves, periodic-cross lump wave propagation, periodic wave propagation, rogue wave propagation, and multiwave propagation were also acquired. Likewise, our solution was also graphically presented, and also their stability was checked.

In this paper, we examine generalized nonlinear Schrödinger equation (GNLSE) for lump, breather lump wave, rogue wave, periodic cross kink wave, lump with one kink, lump with two-kink, interaction between lump periodic and kink wave, periodic cross lump wave, periodic wave and multi-wave. Ansatz transformations will be used to study homoclinic breather, kink cross rational, M-shaped rational, periodic cross rational, M-shaped rational with one kink, M-shaped rational with two-kink, M-shaped interaction with rogue and kink and M-shaped interaction with periodic and kink. We will also study the stability of the obtained solutions. Additionally, we present three-dimensional, two-dimensional, contour, and stream plot illustrations for our graphs. [ABSTRACT FROM AUTHOR]

In this paper, we examine generalized nonlinear Schrödinger equation (GNLSE) for lump, breather lump wave, rogue wave, periodic cross kink wave, lump with one kink, lump with two kink, interaction between lump periodic and kink wave, periodic cross lump wave, periodic wave, and multiwave. Ansatz transformations will be used to study homoclinic breather, kink cross rational, M-shaped rational, periodic cross rational, M-shaped rational with one kink, M-shaped rational with two kink, M-shaped interaction with rogue and kink and M-shaped interaction with periodic and kink. We will also study the stability of the obtained solutions. Additionally, we present 3D, 2D, contour, and stream plot illustrations for our graphs. [ABSTRACT FROM AUTHOR]

Different analytical solutions for Sasa–Satsuma model equation (SSM) in birefringent fibers are investigated in this research like rogue wave, lump, multi-wave, multiple breather solutions, periodic wave, breather lump, periodic cross kink, periodic cross lump, and lump with one and two kinks. By examining the SSM, we can compute the important relationship between the interaction between kink, lump with periodic wave and a variety of exact solutions. To see the behavior of effective waves, we illustrate the pictorial depiction for our retrieve analytical solutions. [ABSTRACT FROM AUTHOR]

This article studies diverse forms of lump-type solutions for coupled nonlinear generalized Zakharov equations (CNL-GZEs) in plasma physics through an appropriate transformation approach and bilinear equations. By utilizing the positive quadratic assumption in the bilinear equation, the lump-type solutions are derived. Similarly, by employing a single exponential transformation in the bilinear equation, the lump one-soliton solutions are derived. Furthermore, by choosing the double exponential ansatz in the bilinear equation, the lump two-soliton solutions are found. Interaction behaviors are observed and we also establish a few new solutions in various dimensions (3D and contour). Furthermore, we compute rogue-wave solutions and lump periodic solutions by employing proper hyperbolic and trigonometric functions. [ABSTRACT FROM AUTHOR]