An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

This research presents the approximate solution of nonlinear Korteweg-de Vries equation of order nine by a hybrid staggered one-dimensional Haar wavelet collocation method. In literature, the underlying equation is derived by generalizing the bilinear form of the standard nonlinear KdV equation. The highest order derivative is approximated by Haar series, whereas the lower order derivatives are attained by integration formula introduced by Chen and Hsiao in 1997. The findings are shown in the form of tables and a figure, demonstrating the proposed technique’s convergence, robustness, and ease of application in a small number of collocation points.

Sub-layer rationale of anomalous layer-shrinkage from atomistic simulations of a fluorinated mesogen

Partially-fluorinated mesogens exhibit some of the most significant de Vries behaviour (anomalously low layer shrinkage at the SmA – SmC transition) reported experimentally, making them of particular interest for technological...

A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

Time Fractional Generalized Korteweg-de Vries Equation: Explicit Series Solutions and Exact Solutions

In this article, an attempt is made to achieve the series solution of the time fractional generalized Korteweg-de Vries equation which leads to a conditionally convergent series solution. We have also resorted to another technique involving conversion of the given fractional partial differential equations to ordinary differential equations by using fractional complex transform. This technique is discussed separately for modified Riemann-Liouville and conformable derivatives. Convergence analysis and graphical view of the obtained solution are demonstrated in this work.

Construcciones de enlace Tail-Head en quichua santiagueño

En muchas lenguas las cláusulas adverbiales iniciales presentan una repetición del predicado de la oración anterior, lo que se conoce como enlace tail-head (tail-head linkage, eth de aquí en más) (Thompson y Longacre, 1985; de Vries, 2005). Este trabajo busca describir las construcciones de eth del quichua santiagueño (quechua) de acuerdo con dos parámetros: a) el grado de solapamiento semántico entre los predicados de la construcción de eth, y b) el grado de integración eventiva de la adverbial inicial con la cláusula principal. El primer parámetro permite identificar construcciones verbatim –con repetición exacta del verbo anterior– y no verbatim –sin repetición exacta–. El segundo parámetro se manifiesta en la forma que adopta la cláusula “cabeza”. Así, se identificaron, por un lado, una forma converbal y, por el otro, cláusulas con los sufijos del sistema de conmutación de la referencia. La interacción entre estos dos parámetros muestra que las diferentes construcciones de eth poseen diversas funciones discursivas, en particular para la coherencia temática (Givón, 2001).

CUBIC DIRAC OPERATORS AND THE STRANGE FREUDENTHAL–DE VRIES FORMULA FOR COLOUR LIE ALGEBRAS

The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition to construct a colour Lie algebra from an ϵ-orthogonal representation of an ϵ-quadratic colour Lie algebra. This is used to prove a strange Freudenthal–de Vries formula for basic colour Lie algebras as well as a Parthasarathy formula for cubic Dirac operators of colour Lie algebras. We calculate the cohomology induced by this Dirac operator, analogously to the algebraic Vogan conjecture proved by Huang and Pandžić.