tl;dr
LocalDate                        // Represent a date-only value, without time-of-day and without time zone.
.now()                           // Capture the current date as seen in the wall-clock time used by the people of a specific region (a time zone). The JVM’s current default time zone is used here. Better to specify explicitly your desired/expected time zone by passing a `ZoneId` argument. Returns a `LocalDate` object.
.with(                           // Generate a new `LocalDate` object based on values of the original but with some adjustment. 
    TemporalAdjusters            // A class that provides some handy pre-defined implementations of `TemporalAdjuster` (note the singular) interface.
    .next(                       // An implementation of `TemporalAdjuster` that jumps to another date on the specified day-of-week.
        DayOfWeek.WEDNESDAY      // Pass one of the seven predefined enum objects, Monday-Sunday.
    )                            // Returns an object implementing `TemporalAdjuster` interface.
)                                // Returns a `LocalDate` object.
Details
Using Java8 Date time API you can easily find the coming Wednesday.
LocalDate nextWed = LocalDate.now().with(TemporalAdjusters.next(DayOfWeek.WEDNESDAY));
next(DayOfWeek dayOfWeek) - Returns the next day-of-week adjuster, which adjusts the date
  to the first occurrence of the specified day-of-week after the date
  being adjusted.
Suppose If you want to get previous Wednesday then,
LocalDate prevWed = LocalDate.now().with(TemporalAdjusters.previous(DayOfWeek.WEDNESDAY));
previous(DayOfWeek dayOfWeek) - Returns the previous day-of-week adjuster, which adjusts
  the date to the first occurrence of the specified day-of-week before
  the date being adjusted.
Suppose If you want to get next or current Wednesday then
LocalDate nextOrSameWed = LocalDate.now().with(TemporalAdjusters.nextOrSame(DayOfWeek.WEDNESDAY));
nextOrSame(DayOfWeek dayOfWeek) - Returns the next-or-same day-of-week
  adjuster, which adjusts the date to the first occurrence of the
  specified day-of-week after the date being adjusted unless it is
  already on that day in which case the same object is returned.
Edit:
You can also pass ZoneId to get the current date from the system clock in the specified time-zone.
ZoneId zoneId = ZoneId.of("UTC");
LocalDate nextWed = LocalDate.now(zoneId).with(TemporalAdjusters.next(DayOfWeek.WEDNESDAY));
For more information refer TemporalAdjusters