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Lump and their interactions with kink, periodic and rogue waves, and periodic cross lump waves will be studied for fifth-order variable coefficient nonlinear-Schrödinger equation in this paper. With the combinations of bilinear, exponent, and trigonometric functions, we'll study different lump soliton solutions. With interaction phenomenon we'll set up some new analytical solutions and also represents them in graphical ways. [ABSTRACT FROM AUTHOR]

In this paper, we study different analytical solutions for long water-wave equation (LWWE) like lump, breathers, rogue waves, periodic cross-kink, periodic wave, lump with one and two-kink, multiwave and periodic-cross lump. We compute the essential relationship between interaction between lump periodic and kink wave, periodic cross-kink and other types of exact solutions by studying the unknown nonlinear evolution equations (NLEEs) for long water wave. We show the graphical representation for our retrieve analytical solutions to observe the behavior of effective waves. [ABSTRACT FROM AUTHOR]

In this article, we construct multi-wave, homoclinic breather, M-shaped rational and periodic cross kink wave solutions for coupled-Higgs equation (CHE) by using distinct transformations. We obtain these solutions with the aid of logarithmic transformations and symbolic computations. Moreover, we also derive some soliton wave solutions for CHE in polynomial forms. These solutions include solitary wave, soliton wave and Jacobi elliptic function solutions and are found by implementing unified technique. We will also discuss the graphical structure of our newly achieved results. [ABSTRACT FROM AUTHOR]

In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan–Kundu–Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations [ABSTRACT FROM AUTHOR]

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing ( G ′ G 2 ) -expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters. [ABSTRACT FROM AUTHOR]

In this paper, we will obtain lump-soliton solution for (1 + 1)-dimensional generalized hyperelastic rod equation, also known as generalized KdV equation by aid of Hirota bilinear method (HBM). We also obtain lump-multisoliton (which is an interaction of lump with one kink or two kink soliton) and lump-periodic solutions (which is formed by an interaction between lump and periodic waves). The dynamics of these solution are examined graphically by selecting significant parameters. [ABSTRACT FROM AUTHOR]

In this article, some novel optical and periodic wave structures are studied to the fractional Schrödinger–Hirota equation with a truncated M -fractional derivative. For this purpose, the integration scheme, which was adopted is fractional extended Fan sub-equation. The optical solitons are observed in single and combined forms, and some other solutions are also fall out during the derivation. Subsequently, the exact solutions demonstrate the effectiveness, efficiency and reliability of the proposed methods, which can be useful for exploring various kind of solutions in the diverse fields of contemporary sciences and engineering. The constraint conditions are utilized, as well as the gained solutions are plugged into the model to verify the results. [ABSTRACT FROM AUTHOR]

In this article, some new traveling wave solutions to the space-time fractional equal-width equation are constructed with the help of the extended Fan sub-equation method. A simple transformation is introduced to convert the fractional order partial differential equation into an ordinary differential equation. As a result, the bright, dark, singular and combined wave solitons are observed for different values of two parameters. Moreover, the graphical representations are also depicted. [ABSTRACT FROM AUTHOR]