In this paper we make a full analysis of the symmetry reductions beam equation by using classical Lie method infinitesimals and nonclassical method. We consider travelling wave depending on form an arbitrary function. have found several new classes solutions that not been considered before: expressed in terms Jacobi elliptic functions, Wadati solitons compactons. Several coherent structures are...

We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multihumped solitons. In particular, we find that stable bound states featuring several field oscillations in each soliton component do exist. This affords stabilization of vector solito...

We study a topology on a space of functions, called sticking topology, with the property to be the weakest among the topologies preserving continuity. In suitable frameworks, this topology preserves borelianity, local integrability, right continuity and other properties. It is coarser than the locally uniform convergence and it allows the presence of gliding humps as we show on examples. We pro...

• Multiaxial fatigue models for notches are analysed. The geometry is an infinite plate with a circular hole. evolution of the predictions increasing hole radius not monotonic. This non-monotonic observed experimentally. work shows analysis several multiaxial notches: Navarro-Rios’ model, which analyses interaction between crack and its associated plastic zone material microstructural barriers,...

A new species of Coulmannia, Coulmannia rossensis, is described from the Ross Sea, Antarctica. It is most similar to Coulmannia ramosae Castelló, 2004, but can easily be distinguished from this species bythe males yielding a pair of granulate humps on the dorsum of the pereonites 1-6 and a single granulate hump on the pereonite 7 and the free pleonite. Coulmannia rossensissp. n. is sexually dim...

In this paper we make a full analysis of the symmetry reductions of a beam equation by using the classical Lie method of infinitesimals and the nonclassical method. We consider travelling wave reductions depending on the form of an arbitrary function. We have found several new classes of solutions that have not been considered before: solutions expressed in terms of Jacobi elliptic functions, W...

Smart water-collecting functions are naturally endowed on biological surfaces with unique wettable microstructures, e.g., beetle back with "alternate hydrophobic, hydrophilic micro-regions", and spider silk with wet-rebuilt "spindle-knot, joint" structures. Enlightened by the creature features, design of bio-inspired surfaces becomes the active issue in need of human beings for fresh water reso...

We consider semilinear parabolic equations of the form ut = uxx + f(u), x ∈ R, t ∈ I, (A) where I = (0,∞) or I = (−∞,∞). Solutions defined for all (x, t) ∈ R2 are referred to as entire solutions. Assuming that f ∈ C1(R) is of a bistable type with stable constant steady states 0 and γ > 0, we show the existence of an entire solution U(x, t) of the following form. For t ≈ −∞, U(·, t) has two hump...