![]() ![]() Although the proposed methods are applicable to a ( n + 1 )-dimensional, n ⩾ 2, scalar wave equation, the discussion will be limited to the case n = 2 for simplicity also, so that comparisons can be made to related recent results in the literature. A modified hybrid spectral representation, based on superpositions of products of forward plane waves moving at a fixed speed c and backward plane waves moving at the speed ν > c, allows in the limit ν → c a smooth transition from superluminal localized waves to paraxial luminal pulsed beams. This means that the linear wave equation in the hydrodynamics can be set up in. In the limiting case ν → c, one recaptures the well-known focus wave mode-type localized wave solutions. The concept of hydrodynamic mass and energy is at first summarized and an. The latter are characterized by arbitrarily high-frequency bands and are suitable for applications in the microwave and optical regime. This representation, which is based on superpositions of products of forward plane waves moving at a fixed speed ν > c and backward plane waves moving at the speed c, is used to construct a large class of finite-energy superluminal-type X-shaped localized waves. A hybrid spectral superposition method is presented that allows a smooth transition between two seemingly distinct classes of localized wave solutions to the homogeneous scalar wave equation in free space specifically, luminal or focus wave modes, and superluminal or X waves. ![]()
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