parameterized by θ ∈ R. But we do not expect that the “sum” of two such solutions will again be a solution. However, the special class of soliton equations, the subject of this article, does have a form of nonlinear superposition. An n-soliton solution is a solution that is asymptotic to a nontrivial sum of n solitary waves ∑n i=1 fi(x− cit) as t → −∞ and to the sum of the same waves ∑n i=1 fi(...

By considering the long-wavelength limit of the regularized long wave ~RLW! equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg–de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...

Background: Solitary fibrous tumor (SFT) is a mesenchymal tumor which is most commonly seen in the pleura; however it can be seen in other organs such as the meninge, gastrointestinal tract, soft tissue, bone, and skin. SFT should be differentiated from other mesenchymal tumors in these organs. Immunohistochemistry plays a pivotal role for the histopathologic diagnosis...

We study the stability of the steady waves forced by a moving localised pressure disturbance in water of finite depth. The steady waves take the form of a downstream wavetrain for subcritical flow, but for supercritical flow there is a solution branch for each specified forcing term, which has two localised solitarylike solutions for each Froude number, a small-amplitude and a large-amplitude s...

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbati...

The bottom-up effects of plant food quality and quantity can affect the growth, survival, and reproduction of herbivores. The larvae of solitary bee pollinators, consumers of nectar and pollen, are also herbivores. Although pollen quantity and quality are known to be important for larval growth, little is known about how nectar quality limits solitary bee performance. By adding different levels...

background: solitary fibrous tumor (sft) is a mesenchymal tumor which is most commonly seen in the pleura; however it can be seen in other organs such as the meninge, gastrointestinal tract, soft tissue, bone, and skin. sft should be differentiated from other mesenchymal tumors in these organs. immunohistochemistry plays a pivotal role for the histopathologic diagnosis of this tumor. currently,...

The solitary wave solution of the quadratic nonlinear Schrd̈inger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution. Keywords—soliton, iterative method, spectral method, plasma

Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. Based on thes...