arXiv subjects
Publications and source records attributed to Danilo V. Ruy.
In this paper, the linear sigma model is studied using a method for finding analytical solutions based on Padé approximants. Using the solutions of two and three traveling waves in 1+3 dimensions we found, we are able to show a solution that is valid for an arbitrary number of bosons and traveling waves.
Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Padé approximants for solving nonlinear partial differential equations without requiring a one-dimensional reduction. This method is applied to the $λϕ^4$ model in 4 dimensions and new solutions are obtained.
Integrable mixed models have been used as a generalization of traditional integrable models. However, a map from a traditional integrable model to a mixed integrable model is not well understood yet. Here, it is studied the relation between the mKdV-Liouville hierarchy and the mKdV hierarchy by employing an extended version of the modified truncation approach. This paper shows some solutions for the mKdV-Liouville hierarchy constructed from the soliton solutions of the mKdV hierarchy. The last section deals with the possibility of define new transcendental functions from the self-similarity reduction of the mKdV-Liouville hierarchy.
We explain the relation between the mixed mKdV/sinh-Gordon model and the Kudryashov's equation. Then, we use the mixed AKNS/Lund-Regge model to find a system of ODEs which is candidate to define a new transcendental function. We also applied the perturbative Painlevé test and presented the local representation for the solution of the system.