Solitary-wave solution for a complex one-dimensional field

Sarker, Sanjoy K.; Trullinger, S. E.; Bishop, A. R.

doi:10.1016/0375-9601(76)90784-2

Cited by 110 publications

(62 citation statements)

References 5 publications

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“…The characteristics of any of these kink defects as well as the structure of the variety as a whole have been elucidated in a long series of papers, see References [2][3][4][5][6][7][8][9][10][11][12]. The moduli space of kinks in an analogous deformation of the linear O(3)-sigma model has also been fully described in [13].…”

Section: Introductionmentioning

confidence: 99%

Kink variety in systems of two coupled scalar fields in two space-time dimensions

2002

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Section: Introductionmentioning

confidence: 99%

Kink variety in systems of two coupled scalar fields in two space-time dimensions

2002

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“…Sarker, Trullinger, and Bishop entered the game by establishing the stability of the two kinds of solution from a energetic point of view [18]: if Ω 2 ∈ (0, 1) the TK2 kinks, being less energetic, are the stable traveling wave solutions and the TK1 kinks should decay to them. If Ω 2 > 1, obviously the TK1 kinks are stable.…”

Section: The Mstb Modelmentioning

confidence: 99%

“…The important point is that, given its supersymmetric origin, a solution of the Hamilton-Jacobi equation (not complete) is always known and trajectories associated to this solution (the superpotential) can be found. This strategy was used in [33] to find a whole family of topological kinks in the BNRT (acronym from [10], in analogy with the MSTB acronym from [17] and [18]) model. The difference with model B, a particular case, is the HJ-separability that allows one to know a complete solution of the HamiltonJacobi equation and, therefore, knowledge of all the trajectories.…”

Section: The Discovery Of New Models Of the Mstb Typementioning

confidence: 99%

“…In particular, we shall choose field theoretical models such that their analogous mechanical system is of Liouville Type I: those two-dimensional mechanical systems such that their Hamilton-Jacobi equation is separable using elliptic coordinates. The simplest and best studied (1+1) dimensional two-component scalar field theory model of this type is the MSTB model (after Montonen, Sarker, Trullinger and Bishop, who first addressed this theory in [17,18]). …”

Section: Introductionmentioning

confidence: 99%

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Generalized MSTB models: Structure and kink varieties

Izquierdo

Guilarte

2008

Physica D: Nonlinear Phenomena

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In this paper we describe the structure of a class of two-component scalar field models in a (1+1) Minkowskian space-time which generalize the well-known Montonen-Sarker-TrullingerBishop -hence MSTB-model. This class includes all the field models whose static field equations are equivalent to the Newton equations of two-dimensional type I Liouville mechanical systems with a discrete set of instability points. We offer a systematic procedure to characterize these models and to identify the solitary wave or kink solutions as homoclinic or heteroclinic trajectories in the analogous mechanical system. This procedure is applied to a one-parametric family of generalized MSTB models with a degree-eight polynomial as potential energy density.

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“…[20,21]). They are referred to as Ising walls when the phase is singular and as Bloch walls when the phase rotates smoothly.…”

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confidence: 99%

Domain walls in nonequilibrium systems and the emergence of persistent patterns

Hagberg

Meron

1993

Phys. Rev. E

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Abstract:Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a consequence, persistent patterns may emerge. We study this mechanism of pattern formation using a non-variational extension of Landau's model for second order phase transitions.

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Solitary-wave solution for a complex one-dimensional field

Cited by 110 publications

References 5 publications

Kink variety in systems of two coupled scalar fields in two space-time dimensions

Kink variety in systems of two coupled scalar fields in two space-time dimensions

Generalized MSTB models: Structure and kink varieties

Domain walls in nonequilibrium systems and the emergence of persistent patterns

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