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This paper seeks to introduce the wave structures and dynamics properties of the perturbed Chen–Lee–Liu equation (PCLLE). Using the traveling wave transformation, we derive the corresponding traveling wave system from the original equation and construct a conserved quantity named as Hamiltonian. Subsequently, we establish periodic solutions and the existence of soliton using the bifurcation method. The bifurcation method is a mathematical technique used to study how the qualitative behavior of a system changes as one or more parameters of the system are varied. It involves analyzing the system's equilibrium points and studying how they behave as the parameters are changed. Finally, we construct the exact traveling wave solutions using the complete discriminant system (CDS) of polynomial method (CDSPM) to explicitly validate our findings. [ABSTRACT FROM AUTHOR]

This paper studies the Lax pair (LP) of the (1 + 1) -dimensional Benjamin–Bona–Mahony equation (BBBE). Based on the LP, initial solution and Darboux transformation (DT), the analytic one-soliton solution will also be obtained for BBBE. This paper contains a bunch of soliton solutions together with bright, dark, periodic, kink, rational, Weierstrass elliptic and Jacobi elliptic solutions for governing model through the newly developed sub-ODE method. The BBBE has a wide range of applications in modeling long surface gravity waves of small amplitude. In addition, we will evaluate generalized breathers, Akhmediev breathers and standard rogue wave solutions for stated model via appropriate ansatz schemes. [ABSTRACT FROM AUTHOR]

This article retrieves diverse forms of localized solutions including lump, lump one-strip, lump two-strip solutions for Schrödinger–Hirota equation with Kerr law nonlinearity through appropriate transformations technique. The proposed model applied in trans-continental and trans-oceanic distances in optical fibers. We compute lump solutions by choosing suitable polynomial function. Under various parameter framework, this lump solution have two forms of multiple-lump waves, particularly, one, and 2-lump waves. Mixed solutions with lump waves and solitons are also evaluated. In addition, we compute Akhmediev breather, generalized breathers and standard rogue wave solutions by using logarithmic transformation. Interaction behaviors are observed and we have also constitute few 3D and contour profiles for new solutions. Furthermore, we evaluate multi-wave soliton solutions for stated model via three wave transformation and logarithmic transformation. [ABSTRACT FROM AUTHOR]

We examine multiwave (MW), rogue wave (RW), periodic wave (PW), homoclinic breather (HB), breather lump wave (BLW), M -shaped rational solutions, lump soliton, kink cross-rational (KCR), periodic cross-kink rational (PCKR), periodic cross-rational (PCR) solutions for the Degasperis–Procesi (DP) equation in shallow water waves through appropriate polynomial function scheme. We also compute some interactions for stated model including interaction of M -shaped soliton with one kink, interactional solution with two kinks also lump soliton with kink one and kink two solutions. Furthermore, we made suitable 3D, 2D and contour profiles via appropriate parameters. [ABSTRACT FROM AUTHOR]

This paper retrieves different types of solutions such as M -shaped rational solutions with one and two kinks, homoclinic breather, multi-waves, periodic cross-kink and kink-cross rational solutions for Radhakrishnan–Kundu–Lakshmanan equation (RKLE). We will study the M -shaped interaction with rogue and kink, we will also obtain the M -shaped interaction with periodic and kink, periodic cross-rational solutions. At the end, we will express the graphical representation for our newly achieved solutions. [ABSTRACT FROM AUTHOR]

We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots. [ABSTRACT FROM AUTHOR]

This manuscript consist of diverse forms of lump: lump one stripe, lump two stripe, generalized breathers, Akhmediev breather, multiwave, M-shaped rational and rogue wave solutions for the complex cubic quintic Ginzburg Landau (CQGL) equation with intrapulse Raman scattering (IRS) via appropriate transformations approach. Furthermore, it includes homoclinic, Ma and Kuznetsov-Ma breather and their relating rogue waves and some interactional solutions, including an interactional approach with the help of the double exponential function. We have elaborated the kink cross-rational (KCR) solutions and periodic cross-rational (KCR) solutions with their graphical slots. We have also constituted some of our solutions in distinct dimensions by means of 3D and contours profiles to anticipate the wave propagation. Parameter domains are delineated in which these exact localized soliton solutions exit in the proposed model. [ABSTRACT FROM AUTHOR]