The solitary-wave interaction mechanism for the good Boussinesq equation is investigated and found to be far more complicated than was previously thought. Three salient features are that solitary waves only exist for a finite range of velocities, that large solitons can turn into so-called antisolitons, and that it is possible for solitons to merge and split. Small solitons, however, appear to be stable. The existence of a potential well is linked to the different behaviors observed between small and large initial conditions.
Abstract. We prove the nonlinear stability and convergence of a fully discrete, pseudospectral scheme for the "good" Boussinesq equation un = -uxxxx + uxx + ("2)xx ■ Numerical comparisons with finite difference schemes are also reported.
Summary. The "good" Boussinesq equation utt = -u .... + Uxx + (u2)~x has recently been found to possess an interesting soliton-interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the "good" Boussinesq equation. Numerical experiments are also reported.
I IntroductionIt has recently been discovered [7] that the interactions of solitary-wave solutions of the "good" Boussinesq equationobey a highly interesting mechanism. The analytic expression of such solutions iswhere 40 and P> 0 are free real parameters and the amplitude A and velocity c of the wave are related to P through the formulasc= +I//I-P 2.Note that 40 determines the initial position of the wave, and that, due to the square root in (1.2), the parameter P can only take values in 0
Se presenta el proceso que ha permitido elaborar distintos modelos de análisis y valoración de textos escolares de matemáticas y, también, ejemplos de su puesta en práctica. Se trata de facilitar al profesorado de educación secundaria la tarea de elegir un libro de texto adecuado al contexto en el que se desarrolla la práctica educativa. Los instrumentos de valoración construidos también pueden constituir herramientas importantes en la elaboración de materiales curriculares por parte del profesorado, e indicadores de calidad profesional. Design and Implementation of Instruments for Analyzing and Assessing Mathematics School Textbooks We present the process that allowed us to elaborate different analysis and evaluation models of mathematics school texts and, also, examples of their application. The aim is to facilitate to secondary education teachers the task of choosing a textbook adapted to the context in which the educational practice is developed. The constructed evaluation instruments can constitute important tools for elaborating curricular materials by teachers as well as indicators of professional quality.Handle: http://hdl.handle.net/10481/14594Nº de citas en WOS (2017): 4 (Citas de 2º orden, 0)Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 1)
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