Abstract
We study a class of noncanonical real scalar field models in $(1+1)$-dimensional flat space-time. We first derive the general criterion for the classical linear stability of an arbitrary static soliton solution of these models. Then we construct first-order formalisms for some typical models and derive the corresponding kink solutions. The linear structures of these solutions are also qualitatively analyzed and compared with the canonical kink solutions.
Highlights
We study a class of noncanonical real scalar field models in (1 + 1)-dimensional flat space-time
We studied the solitary wave solutions of a class of two-dimensional noncanonical scalar field models
We first derived the equation for the linear perturbation around an arbitrary solitary wave solution of the system
Summary
Most of the currently interested noncanonical scalar field models are described by the following action:. Need to derive the linear order equation of δφ(x, t). Since our system is of second order, we are expected to obtain a second-order equation for δφ(x, t). A solution is stable if and only if none of the energy eigenvalues of the corresponding Schrodinger-like equation are negative [28]. The stability issue of K-field models was discussed in literature, none of them offers a general and mathematically simple criterion for stable K-defects. We derive the most general stability condition for a kink solution of our model. One can either expand the action into second-order of δφ, or directly linearize the equation of motion. Both approaches should be equivalent and lead to a same linear perturbation equation. It is necessary to linearize our system with both methods
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