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In this paper, we study chirp-free solitons (dromions) for the higher-order nonlinear Schrödinger equation (HNLSE) having non-Kerr terms with the aid of sub-ODE scheme. We find bright and singular dromion with domain walls, rational and periodic solitons, Weierstrass elliptic functions (WEFs), Jacobi elliptic solutions (JESs) and other solitary wave solutions for our governing model. The Sub-ODE scheme is very useful scheme, providing so many new solitary wave solutions especially JES and WEF solutions. We will also construct graphs of our results in different dimensions along with constraint conditions. [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]

This paper investigates the new solitons and closed form solutions to (3 + 1) dimensional resonant nonlinear Schrödinger equation (RNLSE) that explains the behavior of waves with the effect of group velocity dispersion and resonant nonlinearities in the optical fiber. The soliton solutions in single and combined forms like dark, singular, and dark-singular in mixed form are extracted by means of two innovative integration norms namely extended sinh-Gordon equation expansion and ( G ′ G 2 ) -expansion function methods. Moreover, kink and closed form solutions are also observed under different constraint conditions. By choosing the suitable selection of the parameters, three dimensional, two dimensional, and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]