Rogue waves in electronegative space plasmas: The link between the family of the KdV equations and the nonlinear Schrödinger equation

New Localized and Periodic Solutions to a Korteweg–de Vries Equation with Power Law Nonlinearity: Applications to Some Plasma Models

“…Since this family of the KdV equation has many applications in several branches of science, such as plasma physics, fluid mechanics, nonlinear optics, optical fibers, Bose Einstein condensates, etc. Therefore, the obtained solutions can help a large segment of researchers interested in the field of fluids in general, and plasma physics in particular [28][29][30][31][32][33][34][35][36][37].…”

“…Studying the propagation of ion acoustic waves (IAWs), such as solitary waves in different plasma models with negative ions has been extensively made both experimentally [22][23][24] and theoretically [24][25][26][27][28][29][30] by using the family of KdV equation, mostly the KdV Equation (1) and mKdV Equation (2). Recently, the mKdV/super KdV solitons at supercritical densities in a plasma having two electrons with different temperatures has been investigated [31].…”

Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics

“…Substituting both the stretching and expansion for the independent and dependent quantities into Eqs ( 22 )–( 25 ) and by following the same procedures in Refs. [ 43 , 44 ], we finally obtain the EKdV/Gardner equation where ϕ ≡ ϕ (1) and the coefficients of the quadratic nonlinear term K 1 , cubic nonlinear term K 2 , and dispersion term K 3 are, respectively, given by with Inserting the transformation ϕ ( ξ , τ ) = ϕ ( ζ ) with ζ = ( ξ + λ f τ ) into Eq (25) and integrating the result once over ζ , the following HD equation is obtained [ 39 , 40 ] where λ f characterizes the speed of reference frame and it is arbitrary value, Ϝ 1 = λ f / K 3 , Ϝ 2 = K 1 / (2 K 3 ), Ϝ 3 = K 2 / (3 K 3 ), and Ϝ 4 represents the constant of integration. Applying the boundary conditions for some nonlinear structures such as solitons and shocks as ζ | → ∞, makes Ϝ 4 = 0 which leads to the standard HD equation By analogy, we find that Eq (27) is the same as Eq (21) where its analytical solutions could be found in details in Ref.…”

Interactions of ion acoustic multi-soliton and rogue wave with Bohm quantum potential in degenerate plasma

“…Recently, Hossen et al [8] considered a degenerate epi plasma system consisting of inertial non-relativistic light ions, degenerate electrons, and positrons and noted the effects of tunneling of the plasma particles with the Bohm potential on the propagation of IA waves by deriving the KdV, mKdV, and mixed mKdV (mmKdV) equations. On the other hand, many authors [22][23][24][25][26][27][28][29] have studied the propagation phenomena of the rogue waves by transforming the KdV, mKdV, and mmKdV equations to the corresponding NLS equations. Besides, Mandal et al [30] have investigated only the overtaking collisions and phase shifts of dust acoustic multi-solitions in a fourcomponent dusty plasma.…”

“…However, the interactions between single-and multi-solitons and hence the production of rogue waves along with their structures and dynamics are still unrevealed in the plasmas [8] for better understanding the physical issues observed in space plasmas. [25][26][27][28][29][31][32][33][34][35][36][37][38] Being motivated, for the significance of the problems related to the astrophysical and laboratory plasmas, we study the interaction processes of the IA single-, and multi-solitons, and their phase shifts as well as rogue waves in an unmagnetized plasmas composing degenerate electrons and positrons including Bohm quantum potential and an inertial non-relativistic light ions. The effects of helium ion mass and density, degenerate electrons, and positrons densities and temperatures on the phase shift, interactions among the IA single-and multi-solitons, and the production of rogue waves are investigated.…”