We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in N -dimensions that follows from an action principle. Further, we show that our N -dimensional Lagrangian formulation leads to a subclass of the equations discussed recently by Rosenau, Hyman and Staley.

We find and analyze bound dipole solitary solutions in media with anisotropic nonlocal photorefractive material response. The dipole solutions consist of two elliptically shaped Gaussian-type beams separated by several diameters, and with a p phase shift between their fields. Spatial evolution of two initially round Gaussian beams and their convergence to the above dipole solution is demonstrat...

The criterion of modulational instability the second order bright solitary wave is studied in this article. Principle consists initially seeking all solutions type which verify nonlinear partial differential equation governs dynamics propagation flattened optical fibers. When reference solution to be subjected a disturbance identified, next step establishing condition stability/instability.

The Broer-Kaup equation is one of many equations describing some phenomena shallow water wave. There are errors in scientific research because the existence non-smooth boundaries. In this paper, we generalize to fractal space and establish variational formulations through semi-inverse method. acquired formulation reveals conservation laws an energy form suggests possible solution structures mor...

In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support. This is the second in a series of two p...

introduction: solitary fibrous tumor is a rare, mesenchymal neoplasm that has been reported in numerous sites. occurrence in the parotid gland is exceedingly rare.   case report: a 53-year-old man with a 2 cm solitary fibrous tumor of the left parotid gland, that was observed clinically and operatively and thought to be a neoplasm arising from stensen's duct, is described. a pre-operative ...

conclusions this is the first case of sft of the retroperitoneum removed laparoscopically. the laparoscopic approach is useful for the advantages of minimally invasive surgery especially in case of peduncolate tumor as the case reported. case presentation a 29-year-old female, was admitted in the gynaecology and obstetrics unit, for suspected pelvic tumor. ct scan showed a mass with hypervascul...

solitary plasmacytoma of bone is a rare malignant tumor mostly involving the axial skeleton. the tumor occurs in middle- aged or elderly people (mean age: 55 years) and has a high risk of progression to multiple myeloma. radiotherapy is the preferred treatment for this disease. we report a case of recurrent solitary plasmacytoma of the fourth lumbar vertebra in a 35-year-old male. the patient s...

In this work, the relativistic non-standard Lagrangian densities (k-fields) with massless solutions are generally introduced. Such not necessarily energetically stable. However, in $$3+1$$ dimensions, we introduce a new k-field model that results single non-topological solitary wave solution. This special solution is stable; is, any arbitrary deformation above its background leads to an increas...