[1] A sequence of three internal solitary waves of elevation were observed propagating shoreward along a near-bottom density interface over Oregon’s continental shelf. These waves are highly turbulent and coincide with enhanced optical backscatter, consistent with increased suspended sediments in the bottom boundary layer. Nonlinear solitary wave solutions are employed to estimate wave speeds a...

Strongly nonlinear phononic crystals were assembled from stainless steel spheres. Single solitary waves and splitting of an initial pulse into a train of solitary waves were investigated in different viscous media using motor oil and non-aqueous glycerol to introduce a controlled viscous dissipation. Experimental results indicate that the presence of a viscous fluid dramatically altered the spl...

Surface wave dynamics of vertical falling films under monochromatic-frequency flowrate-forcing perturbations is computed by the direct simulation of Navier–Stokes equations using the Volume of Fluid (VOF) method to track free surfaces and the Continuum Surface Force (CSF) model to account for dynamic boundary conditions at free surfaces. The numerical VOF–CSF model is completely formulated, and...

For the one-dimensional nonlinear Schrödinger equations with parity-time (PT) symmetric potentials, it is shown that when a real symmetric potential is perturbed by weak PT-symmetric perturbations, continuous families of asymmetric solitary waves in the real potential are destroyed. It is also shown that in the same model with a general PT-symmetric potential, symmetry breaking of PT-symmetric ...

We study the spectral (in)stability of one-dimensional solitary and cnoidal waves of various Boussinesq systems. These systems model three-dimensional water waves (i.e., the surface is two-dimensional) with or without surface tension. We present the results of numerous computations examining the spectra related to the linear stability problem for both stationary solitary and cnoidal waves with ...

We present a detailed analysis of finite energy solitary waves in twoand three-dimensional nonlinear periodic structures exhibiting a complete photonic band gap. Solitary waves in photonic crystals with a twodimensional ~2D! square and triangular symmetry group as well as a 3D fcc symmetry group are described in terms of an effective nonlinear Dirac equation derived using the slowly varying env...

Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that ...

An explanation is given for previous numerical results which suggest a certain bifurcation of ‘vector solitons’ from scalar (single-component) solitary waves in coupled nonlinear Schrödinger (NLS) systems. The bifurcation in question is nonlocal in the sense that the vector soliton does not have a small-amplitude component, but instead approaches a solitary wave of one component with two infini...

We prove that the Cauchy problem for a certain sixth order hyperelastic dispersive equation is globally well-posed in a natural space. We also show that there exist solitary wave solutions u(x, y, t) = φc(x − ct, y) that come from an associated variational problem. Such solitary waves are nonlinearly stable in the sense that if a solution is initially close to the set of such solitary waves, it...

Transverse instabilities correspond to a class of perturbations traveling in a direction transverse to the direction of the basic solitary wave. Solitary waves traveling in one space direction generally come in one-parameter families. We embed them in a two-parameter family and deduce a new geometric condition for transverse instability of solitary waves. This condition is universal in the sens...