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Motivated by recent experimental and theoretical results on optical X-waves,we propose a new type of waveforms in 2D and 3D discrete media -- multi-leggedextended nonlinear structures (ENS), built as arrays of lattice solitons (tilesor stones, in the 2D and 3D cases, respectively). First, we study the stabilityof the tiles and stones analytically, and then extend them numerically tocomplete ENS forms for both 2D and 3D lattices. The predicted patterns arerelevant to a variety of physical settings, such as Bose-Einstein condensatesin deep optical lattices, lattices built of microresonators, photorefractivecrystals with optically induced lattices (in the 2D case) and others.Comment: 4 pages, 4 figure

physical review. e, statistical, nonlinear and soft matter physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Y</mml:mi></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Z</mml:mi></mml:mrow></mml:math>waves: Extended structures in nonlinear lattices

X,Y, andZwaves: Extended structures in nonlinear lattices