Topological 1-soliton solution of the Biswas–Milovic equation with power law nonlinearity

Explicit bright and dark solitons for the variable coefficient Biswas–Milovic equation with competing nonlinearity

“…The dimensionless form of the BM equation that is going to be studied in this paper is given by [21,22] …”

“…A c c e p t e d M a n u s c r i p t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 where the width B, wave number κ, phase shift θ and amplitude A 0 are all constants, while the frequency ω(t) and the velocity v(t) of the soliton are given in (20) and (22). The constraint relation between the variable parameters a(t), b(t) and α(t) for the existence of soliton is shown in (24).…”

“…In case of dark solitons, the phase changes for large spatial distance [17,19,20,21,22,23,24]. In this section, the dark solitons for the variable coefficient BM equation will be obtained for four forms of nonlinearity discussed above.…”

“…The study of solitons finds application in various branches of physical and natural sciences such as plasma physics, nonlinear optics, nuclear physics, light wave communication technology, photonics, condensed matter physics and various others [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] for the past few decades. The delicate balance between nonlinearity and dispersion effects in the medium causes envelope soliton which are stable nonlinear wave packets that maintains their shapes during the propagation in a nonlinear dispersive medium [25].…”

“…Some of the commonly studied tools are the Adomian decomposition method , homotopy perturbation method , exp-function method , variational iteration method, tanh-sech method , sine-cosine method, (G ′ /G)-expansion method and many more [5,6,7,8,9,10,11,12,13,14,15,16]. In this paper the solitary wave ansatz method is generalized in context of doubly periodic Jacobi elliptic functions and will be utilized to carry out integration of the Biswas-Milovic (BM) equation [21,22]. In 2009, the BM equation first appeared as the generalization to the nonlinear Schrödinger equation (NLSE) which can be found in the context of Nonlinear optics, Plasma physics, Biochemistry and others [21].…”