Quasiclassical localization of wave packets in nonlinear Schrödinger systems

Soliton Structures in a Molecular Chain Model with Saturation

“…We will follow the findings of the paper [15] As it is well known, our system is closely related to the phi-six theory, that shows several important behavior in nuclear hydrodynamics, ferromagnetism, phase transitions and other branches of physics and natural sciences [11]. The equation of motion that we will analyze in the context of self localization is the equation (12) obtained above.…”

“…Next, we can use some results concerning the possibility of stabilizations of those types of solitons we have found in the section A and B for those distribution of excitations with non-topological charges. We will follow the findings of the paper [15] As it is well known, our system is closely related to the phi-six theory, that shows several important behavior in nuclear hydrodynamics, ferromagnetism, phase transitions and other branches of physics and natural sciences [11]. The equation of motion that we will analyze in the context of self localization is the equation ( 12) obtained above.…”

“…where Φ ≡ ψ * ψ , the dimension of the space is D and with suitable change of parameters we use the potential part of the energy as [11,15] …”

“…The constant solutions of the equation (11) at A = − 1 2 undergoes a supercritical bifurcation. For analyzing the self-localizations of soliton structures we will evaluate the behavior of the following functional B(t) [11,15] …”

“…As we are concerned with solitons in one dimensional case for the molecular system, finally making D = 1, and evaluating the conditions under self-localization of soliton structures we finally obtain that following conditions [15] If…”