1,721,063 research outputs found
Exact Solutions of Hydrodynamic Type Equations Having Infinitely Many Conserved Densities
No full textKodama, Yuji. (1989). Exact Solutions of Hydrodynamic Type Equations Having Infinitely Many Conserved Densities. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4928
A Method for Solving the Dispersionless KP Hierarchy and its Exact Solutions II
No full textKodama, Yuji; Gibbons, John. (1989). A Method for Solving the Dispersionless KP Hierarchy and its Exact Solutions II. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4927
Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin
Full text linkThere is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive
spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media.
Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave
solutions of the ð2 þ 1ÞD nonlinear Schrödinger equation. Dark lumps represent multidimensional holes
of light on a continuous wave background.We analytically derive the dark lumps from the hydrodynamic
exact soliton solutions of the ð2 þ 1ÞD shallow water Kadomtsev-Petviashvili model, inheriting their
complex interaction properties. This finding opens a novel path for the excitation and control of optical
spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave
phenomena
Critical points, Lauricella functions and Whitham-type equations
No full textA large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of Lauricelle type functions
Optical Spatio-Temporal Dynamics of Hydrodynamic Origin
No full textThere is considerable fundamental and applicative interest in obtaining non-diffractive and non-dispersive spatio-temporal localized wave packets propagating in optical cubic nonlinear or Kerr media [1-3]. Here, we analytically predict the existence of a novel family of spatio-temporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrodinger equation (NLSE). Dark lumps represent multi-dimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili (KP) model [4,5], inheriting their complex interaction properties (see Fig. 1). Our finding opens a novel path for the excitation and control of optical multidimensional extreme wave phenomena of hydrodynamic footprint [6].
[1] R. Boyd, Nonlinear Optics, 3rd ed. (Academic Press,
London, 2008).
[2] Y. Silberberg, Opt. Lett. 15, 1282 (1990).
[3] C. Conti et al., Phys. Rev. Lett.
90, 170406 (2003).
[4] S.V. Manakov et al., Phys. Lett. A 63, 205 (1977).
[5] Z. Lu, et al. Wave Motion 40, 1223 (2004).
[6] F. Baronio, S. Wabnitz, and Y. Kodama, Arxiv 1602.08464 (2016)
Optical Kerr spatiotemporal dark extreme waves
Full text linkWe study the existence and propagation of multidimensional dark non-diffractive and non-dispersive spatiotemporal optical wave-packets in nonlinear Kerr media. We report analytically and confirm numerically the properties of spatiotemporal dark lines, X solitary waves and lump solutions of the (2 + 1)D nonlinear Schrodinger equation (NLSE). Dark lines, X waves and lumps represent holes of light on a continuous wave background. These solitary waves are derived by exploiting the connection between the (2 + 1)D NLSE and a well-known equation of hydrodynamics, namely the (2+1)D Kadomtsev-Petviashvili (KP) equation. This finding opens a novel path for the excitation and control of spatiotemporal optical solitary and rogue waves, of hydrodynamic nature
Spatiotemporal optical dark X solitary waves
Full text linkWe introduce spatiotemporal optical dark X solitary waves of the (2 + 1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics
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